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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
A000201
Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.
[ "1", "3", "4", "6", "8", "9", "11", "12", "14", "16", "17", "19", "21", "22", "24", "25", "27", "29", "30", "32", "33", "35", "37", "38", "40", "42", "43", "45", "46", "48", "50", "51", "53", "55", "56", "58", "59", "61", "63", "64", "66", "67", "69", "71", "72", "74", "76", "77", "79", "80", "82", "84", "85", "87", "88", "90", "92", "93", "95", "97", "98", "100", "101", "103", "105", "106", "108", "110" ]
[ "nonn", "easy", "nice", "changed" ]
294
1
2
[ "A000201", "A001030", "A001468", "A001950", "A002251", "A003622", "A003623", "A003842", "A003849", "A004641", "A005206", "A005614", "A007067", "A014675", "A022342", "A026242", "A026274", "A035336", "A058066", "A088462", "A096270", "A101864", "A114986", "A124841", "A183110", "A185615", "A276854", "A329825", "A342279" ]
[ "M2322", "N0917" ]
N. J. A. Sloane
2025-04-18T03:18:07
oeisdata/seq/A000/A000201.seq
a14062ba14855ebac75a4a06f9004c37
A000202
a(8i+j) = 13i + a(j), where 1<=j<=8.
[ "1", "3", "4", "6", "8", "9", "11", "12", "14", "16", "17", "19", "21", "22", "24", "25", "27", "29", "30", "32", "34", "35", "37", "38", "40", "42", "43", "45", "47", "48", "50", "51", "53", "55", "56", "58", "60", "61", "63", "64", "66", "68", "69", "71", "73", "74", "76", "77", "79", "81", "82", "84", "86", "87", "89", "90", "92", "94", "95", "97", "99", "100", "102", "103", "105", "107", "108", "110" ]
[ "nonn", "easy" ]
41
1
2
[ "A000045", "A000201", "A000202", "A066096", "A090908" ]
[ "M2323", "N0918" ]
N. J. A. Sloane
2025-01-05T19:51:31
oeisdata/seq/A000/A000202.seq
6c09430f16748be52d40dc6e00c0c055
A000203
a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).
[ "1", "3", "4", "7", "6", "12", "8", "15", "13", "18", "12", "28", "14", "24", "24", "31", "18", "39", "20", "42", "32", "36", "24", "60", "31", "42", "40", "56", "30", "72", "32", "63", "48", "54", "48", "91", "38", "60", "56", "90", "42", "96", "44", "84", "78", "72", "48", "124", "57", "93", "72", "98", "54", "120", "72", "120", "80", "90", "60", "168", "62", "96", "104", "127", "84", "144", "68", "126", "96", "144" ]
[ "easy", "core", "nonn", "nice", "mult" ]
571
1
2
[ "A000005", "A000203", "A000593", "A001001", "A001065", "A001157", "A001158", "A001159", "A001160", "A001227", "A001318", "A001615", "A002093", "A002192", "A002659", "A006352", "A007609", "A007955", "A008438", "A009194", "A013954", "A013955", "A013956", "A013957", "A013958", "A013959", "A013960", "A013961", "A013962", "A013963", "A013964", "A013965", "A013966", "A013967", "A013968", "A013969", "A013970", "A013971", "A013972", "A024916", "A027748", "A034448", "A034885", "A039653", "A050449", "A050452", "A051731", "A053866", "A054533", "A054973", "A057641", "A062731", "A069192", "A074400", "A082062", "A083238", "A083728", "A088580", "A124010", "A127093", "A144613", "A144614", "A144615", "A144736", "A146076", "A147843", "A158902", "A158951", "A174740", "A179931", "A192795", "A281959" ]
[ "M2329", "N0921" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000203.seq
cd67c4d2d5782efc8b7740049ca23874
A000204
Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.
[ "1", "3", "4", "7", "11", "18", "29", "47", "76", "123", "199", "322", "521", "843", "1364", "2207", "3571", "5778", "9349", "15127", "24476", "39603", "64079", "103682", "167761", "271443", "439204", "710647", "1149851", "1860498", "3010349", "4870847", "7881196", "12752043", "20633239", "33385282", "54018521", "87403803", "141422324" ]
[ "core", "easy", "nonn", "nice" ]
302
1
2
[ "A000032", "A000045", "A000079", "A000108", "A000204", "A001609", "A003269", "A003520", "A005708", "A005709", "A005710", "A006206", "A014097", "A027960", "A061084", "A090946", "A094216", "A094638", "A099731", "A100492", "A101032", "A101033" ]
[ "M2341", "N0924" ]
N. J. A. Sloane
2025-04-05T23:17:32
oeisdata/seq/A000/A000204.seq
655481c03db4d08321ad89e1c775214e
A000205
Number of positive integers <= 2^n of form x^2 + 3 y^2.
[ "1", "1", "3", "4", "8", "14", "25", "45", "82", "151", "282", "531", "1003", "1907", "3645", "6993", "13456", "25978", "50248", "97446", "189291", "368338", "717804", "1400699", "2736534", "5352182", "10478044", "20531668", "40264582", "79022464", "155196838", "304997408", "599752463", "1180027022", "2322950591", "4575114295" ]
[ "nonn" ]
28
0
3
[ "A000050", "A000205", "A003136" ]
[ "M2350", "N0928" ]
N. J. A. Sloane
2022-04-29T12:15:21
oeisdata/seq/A000/A000205.seq
162a530bfee59127d7927d4a7fda3e4c
A000206
Even sequences with period 2n.
[ "1", "1", "3", "4", "12", "22", "71", "181", "618", "1957", "6966", "24367", "89010", "324766", "1204815", "4482400", "16802826", "63195016", "238711285", "904338163", "3436380192", "13089961012", "49979421837", "191221556269", "733014218506", "2814758323498", "10825986453978", "41700030726757", "160842946895004" ]
[ "nonn", "easy", "nice" ]
34
0
3
[ "A000011", "A000013", "A000206", "A000208" ]
[ "M2372", "N0940" ]
N. J. A. Sloane
2022-04-30T12:18:27
oeisdata/seq/A000/A000206.seq
6ca501404cc3b6e76cb2bf53df59d4ef
A000207
Number of inequivalent ways of dissecting a regular (n+2)-gon into n triangles by n-1 non-intersecting diagonals under rotations and reflections; also the number of (unlabeled) maximal outerplanar graphs on n+2 vertices.
[ "1", "1", "1", "3", "4", "12", "27", "82", "228", "733", "2282", "7528", "24834", "83898", "285357", "983244", "3412420", "11944614", "42080170", "149197152", "531883768", "1905930975", "6861221666", "24806004996", "90036148954", "327989004892", "1198854697588", "4395801203290", "16165198379984", "59609171366326", "220373278174641" ]
[ "nonn", "nice", "easy" ]
140
1
4
[ "A000207", "A000577", "A001683", "A005036", "A007173", "A070765", "A097998", "A097999", "A098000", "A111563", "A111564", "A111757", "A111758", "A111759", "A169808", "A208355", "A295260", "A369314" ]
[ "M2375", "N0942" ]
N. J. A. Sloane
2024-07-28T16:36:13
oeisdata/seq/A000/A000207.seq
5606fdc5c58bbbfd4df5dae95a0c140b
A000208
Number of even sequences with period 2n.
[ "1", "1", "3", "4", "12", "28", "94", "298", "1044", "3658", "13164", "47710", "174948", "645436", "2397342", "8948416", "33556500", "126324496", "477225962", "1808414182", "6871973952", "26178873448", "99955697946", "382438918234", "1466015854100", "5629499869780" ]
[ "nonn", "easy", "nice" ]
39
0
3
[ "A000013", "A000206", "A000208" ]
[ "M2377", "N0943" ]
N. J. A. Sloane
2022-04-30T12:18:31
oeisdata/seq/A000/A000208.seq
a44573046038a2b587b852c949bb874d
A000209
Nearest integer to tan n.
[ "0", "2", "-2", "0", "1", "-3", "0", "1", "-7", "0", "1", "-226", "-1", "0", "7", "-1", "0", "3", "-1", "0", "2", "-2", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-75", "-1", "0", "8", "-1", "0", "4", "-1", "0", "2", "-1", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-45", "-1", "0", "8", "-1", "0", "4", "-1", "0", "2", "-1", "0", "2", "-2", "0", "1", "-3", "0", "1", "-6", "0", "1", "-32", "-1", "0", "9", "-1" ]
[ "sign" ]
26
0
2
null
null
N. J. A. Sloane
2023-10-28T12:03:11
oeisdata/seq/A000/A000209.seq
6977d5b0bdfa03f26781a8a92251b7a3
A000210
A Beatty sequence: floor(n*(e-1)).
[ "1", "3", "5", "6", "8", "10", "12", "13", "15", "17", "18", "20", "22", "24", "25", "27", "29", "30", "32", "34", "36", "37", "39", "41", "42", "44", "46", "48", "49", "51", "53", "54", "56", "58", "60", "61", "63", "65", "67", "68", "70", "72", "73", "75", "77", "79", "80", "82", "84", "85", "87", "89", "91", "92", "94", "96", "97", "99", "101", "103", "104", "106", "108", "109", "111", "113", "115", "116" ]
[ "nonn" ]
40
1
2
null
[ "M2393", "N0950" ]
N. J. A. Sloane
2017-06-30T01:49:05
oeisdata/seq/A000/A000210.seq
ae107ebea954748d8db66971dd16b071
A000211
a(n) = a(n-1) + a(n-2) - 2, a(0) = 4, a(1) = 3.
[ "4", "3", "5", "6", "9", "13", "20", "31", "49", "78", "125", "201", "324", "523", "845", "1366", "2209", "3573", "5780", "9351", "15129", "24478", "39605", "64081", "103684", "167763", "271445", "439206", "710649", "1149853", "1860500", "3010351", "4870849", "7881198" ]
[ "nonn", "easy", "nice" ]
85
0
1
[ "A000204", "A000211" ]
[ "M2396", "N0953" ]
N. J. A. Sloane
2022-04-13T13:25:14
oeisdata/seq/A000/A000211.seq
bc3d0baa8e453da7c6d63b569893a979
A000212
a(n) = floor(n^2/3).
[ "0", "0", "1", "3", "5", "8", "12", "16", "21", "27", "33", "40", "48", "56", "65", "75", "85", "96", "108", "120", "133", "147", "161", "176", "192", "208", "225", "243", "261", "280", "300", "320", "341", "363", "385", "408", "432", "456", "481", "507", "533", "560", "588", "616", "645", "675", "705", "736", "768", "800", "833", "867", "901", "936" ]
[ "nonn", "easy" ]
234
0
4
[ "A000212", "A000217", "A000290", "A001353", "A001399", "A001523", "A001840", "A002620", "A004523", "A005408", "A007052", "A007304", "A007590", "A007980", "A011782", "A014612", "A033436", "A033437", "A033438", "A033439", "A033440", "A033441", "A033442", "A033443", "A033444", "A056827", "A056834", "A056838", "A056865", "A069905", "A072706", "A115981", "A118013", "A118015", "A130519", "A184535", "A211540", "A220377", "A238738", "A332743", "A335373", "A337453", "A337459", "A337460", "A337461", "A337561", "A337603", "A337604" ]
[ "M2439", "N0966" ]
N. J. A. Sloane
2025-02-24T10:52:09
oeisdata/seq/A000/A000212.seq
2aef5ff3b4488cd74540b0e943ab16eb
A000213
Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.
[ "1", "1", "1", "3", "5", "9", "17", "31", "57", "105", "193", "355", "653", "1201", "2209", "4063", "7473", "13745", "25281", "46499", "85525", "157305", "289329", "532159", "978793", "1800281", "3311233", "6090307", "11201821", "20603361", "37895489", "69700671", "128199521", "235795681", "433695873", "797691075", "1467182629" ]
[ "nonn", "easy", "nice" ]
239
0
4
[ "A000073", "A000213", "A000288", "A000322", "A000383", "A046735", "A060455", "A180735", "A186190" ]
[ "M2454", "N0975" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000213.seq
29a241dc00dca40554e00e87550a3d30
A000214
Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).
[ "3", "5", "10", "32", "382", "15768919", "16224999167506438730294", "84575066435667906978109556031081616704183639810103015118" ]
[ "nonn", "nice", "easy" ]
38
1
1
[ "A000214", "A000585" ]
[ "M2470", "N0980" ]
N. J. A. Sloane
2019-04-14T02:10:09
oeisdata/seq/A000/A000214.seq
c598b3bff5c1eb166a36224b1ef54015
A000215
Fermat numbers: a(n) = 2^(2^n) + 1.
[ "3", "5", "17", "257", "65537", "4294967297", "18446744073709551617", "340282366920938463463374607431768211457", "115792089237316195423570985008687907853269984665640564039457584007913129639937" ]
[ "nonn", "easy", "nice" ]
300
0
1
[ "A000058", "A000120", "A000215", "A000225", "A001146", "A004249", "A006943", "A007814", "A014118", "A019434", "A050922", "A051158", "A051179", "A063486", "A073617", "A077585", "A080176", "A085866", "A125134", "A220570", "A220571", "A220627", "A242619", "A242620", "A249119", "A257916", "A257917" ]
[ "M2503", "N0990" ]
N. J. A. Sloane
2025-03-30T09:54:29
oeisdata/seq/A000/A000215.seq
e5b3d7d47326c3577de7a485c81d05f6
A000216
Take sum of squares of digits of previous term, starting with 2.
[ "2", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37" ]
[ "nonn", "base", "easy" ]
60
1
1
[ "A000216", "A000218", "A000221", "A003132", "A003621", "A007770", "A008460", "A008462", "A008463", "A031176", "A039943", "A080709", "A099645", "A122065", "A139566" ]
null
N. J. A. Sloane
2023-12-14T06:01:56
oeisdata/seq/A000/A000216.seq
59ed9b98ff23e96263061be7e0136a00
A000217
Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.
[ "0", "1", "3", "6", "10", "15", "21", "28", "36", "45", "55", "66", "78", "91", "105", "120", "136", "153", "171", "190", "210", "231", "253", "276", "300", "325", "351", "378", "406", "435", "465", "496", "528", "561", "595", "630", "666", "703", "741", "780", "820", "861", "903", "946", "990", "1035", "1081", "1128", "1176", "1225", "1275", "1326", "1378", "1431" ]
[ "nonn", "core", "easy", "nice", "changed" ]
1,863
0
3
[ "A000096", "A000124", "A000212", "A000217", "A000290", "A000292", "A000326", "A000330", "A000384", "A000396", "A000566", "A000567", "A000668", "A000718", "A000746", "A001082", "A001106", "A001107", "A001318", "A001399", "A001477", "A001788", "A001840", "A002024", "A002378", "A002415", "A002817", "A003056", "A004526", "A005563", "A006011", "A007304", "A007318", "A007501", "A008291", "A008953", "A008954", "A010054", "A011782", "A013589", "A016754", "A028347", "A036666", "A046092", "A050536", "A050542", "A050548", "A050909", "A051942", "A055998", "A055999", "A056000", "A056115", "A056119", "A056121", "A056126", "A060544", "A062717", "A067728", "A069905", "A075528", "A085787", "A087475", "A099174", "A101859", "A104712", "A109613", "A110449", "A110555", "A130534", "A132440", "A140091", "A140681", "A143320", "A156040", "A195152", "A210569", "A211540", "A212331", "A220377", "A238363", "A245031", "A245300", "A307719", "A337461", "A337483", "A337604" ]
[ "M2535", "N1002" ]
N. J. A. Sloane
2025-04-17T09:48:11
oeisdata/seq/A000/A000217.seq
45815f5a9253bfcce9462c46ba9f92b4
A000218
Take sum of squares of digits of previous term; start with 3.
[ "3", "9", "81", "65", "61", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37" ]
[ "nonn", "base", "easy" ]
47
1
1
[ "A000216", "A000218", "A000221", "A003132", "A003621", "A007770", "A008460", "A008462", "A008463", "A031176", "A039943", "A080709", "A099645", "A122065", "A139566" ]
null
N. J. A. Sloane
2022-09-08T08:44:27
oeisdata/seq/A000/A000218.seq
0230a975240221ddfbbbc2b89254e1e1
A000219
Number of plane partitions (or planar partitions) of n.
[ "1", "1", "3", "6", "13", "24", "48", "86", "160", "282", "500", "859", "1479", "2485", "4167", "6879", "11297", "18334", "29601", "47330", "75278", "118794", "186475", "290783", "451194", "696033", "1068745", "1632658", "2483234", "3759612", "5668963", "8512309", "12733429", "18974973", "28175955", "41691046", "61484961", "90379784", "132441995", "193487501", "281846923" ]
[ "nonn", "nice", "easy", "core" ]
270
0
3
[ "A000041", "A000219", "A000784", "A000785", "A000786", "A000990", "A000991", "A001157", "A001452", "A002799", "A005380", "A005987", "A023871", "A023878", "A026007", "A048141", "A048142", "A089300", "A089353", "A091298", "A091438", "A144048", "A161870", "A162453", "A191659", "A191660", "A191661", "A193427", "A225196", "A225197", "A225198", "A225199", "A249386", "A249387", "A255610", "A255611", "A255612", "A255613", "A255614", "A285216" ]
[ "M2566", "N1016" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000219.seq
c26e2b90ba653e62916bcc4ba85d794e
A000220
Number of asymmetric trees with n nodes (also called identity trees).
[ "1", "0", "0", "0", "0", "0", "1", "1", "3", "6", "15", "29", "67", "139", "310", "667", "1480", "3244", "7241", "16104", "36192", "81435", "184452", "418870", "955860", "2187664", "5025990", "11580130", "26765230", "62027433", "144133676", "335731381", "783859852", "1834104934", "4300433063", "10102854473", "23778351222" ]
[ "nonn", "nice" ]
49
1
9
[ "A000055", "A000081", "A000220", "A004111", "A035056", "A246169" ]
[ "M2583", "N1022" ]
N. J. A. Sloane
2023-10-27T18:22:09
oeisdata/seq/A000/A000220.seq
2c3de4450671b3013652c0de09e416ba
A000221
Take sum of squares of digits of previous term; start with 5.
[ "5", "25", "29", "85", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145", "42", "20", "4", "16", "37", "58", "89", "145" ]
[ "nonn", "base", "easy", "nice" ]
46
1
1
[ "A000216", "A000218", "A000221", "A003132", "A003621", "A007770", "A008460", "A008462", "A008463", "A031176", "A039943", "A080709", "A099645", "A122065", "A139566" ]
null
N. J. A. Sloane
2022-09-08T08:44:27
oeisdata/seq/A000/A000221.seq
a559860bf164bf8cd0a148bed60a65fe
A000222
Coefficients of ménage hit polynomials.
[ "0", "0", "1", "3", "6", "38", "213", "1479", "11692", "104364", "1036809", "11344859", "135548466", "1755739218", "24504637741", "366596136399", "5852040379224", "99283915922264", "1783921946910417", "33840669046326579", "675849838112277598", "14174636583759324798" ]
[ "nonn" ]
33
0
4
[ "A000222", "A058057" ]
[ "M2602", "N1029" ]
N. J. A. Sloane, Simon Plouffe
2019-06-13T19:56:11
oeisdata/seq/A000/A000222.seq
56817d0889f9cd933e00d40e41f47e73
A000223
Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).
[ "3", "7", "10", "19", "32", "34", "37", "51", "81", "119", "122", "134", "157", "160", "161", "174", "221", "252", "254", "294", "305", "309", "364", "371", "405", "580", "682", "734", "756", "763", "776", "959", "1028", "1105", "1120", "1170", "1205", "1550", "1570", "1576", "1851", "1930", "2028", "2404", "2411", "2565", "2675", "2895", "2905", "2940", "3133", "3211", "3240", "3428" ]
[ "nonn" ]
34
1
1
[ "A000036", "A000092", "A000099", "A000223", "A000323", "A000413" ]
[ "M2619", "N1036" ]
N. J. A. Sloane
2022-05-03T11:06:05
oeisdata/seq/A000/A000223.seq
c608767e5c663e48c47b9699bfa635a8
A000224
Number of squares mod n.
[ "1", "2", "2", "2", "3", "4", "4", "3", "4", "6", "6", "4", "7", "8", "6", "4", "9", "8", "10", "6", "8", "12", "12", "6", "11", "14", "11", "8", "15", "12", "16", "7", "12", "18", "12", "8", "19", "20", "14", "9", "21", "16", "22", "12", "12", "24", "24", "8", "22", "22", "18", "14", "27", "22", "18", "12", "20", "30", "30", "12", "31", "32", "16", "12", "21", "24", "34", "18", "24", "24", "36", "12" ]
[ "nonn", "easy", "nice", "mult", "changed" ]
105
1
2
[ "A000224", "A046530", "A052273", "A052274", "A052275", "A085310", "A085311", "A085312", "A085313", "A085314", "A095972", "A228849" ]
null
N. J. A. Sloane
2025-04-27T01:05:12
oeisdata/seq/A000/A000224.seq
c8868412e648a6a80043bf00432c8a19
A000225
a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)
[ "0", "1", "3", "7", "15", "31", "63", "127", "255", "511", "1023", "2047", "4095", "8191", "16383", "32767", "65535", "131071", "262143", "524287", "1048575", "2097151", "4194303", "8388607", "16777215", "33554431", "67108863", "134217727", "268435455", "536870911", "1073741823", "2147483647", "4294967295", "8589934591" ]
[ "nonn", "easy", "core", "nice", "changed" ]
826
0
3
[ "A000043", "A000079", "A000203", "A000225", "A000668", "A000918", "A001045", "A001348", "A008277", "A008969", "A009545", "A016189", "A029858", "A048993", "A051885", "A052955", "A058809", "A062318", "A083329", "A085104", "A112492", "A118654", "A130330", "A132781", "A140576", "A144081", "A165804", "A180516", "A181287", "A181288", "A181303", "A239473", "A279396", "A375256" ]
[ "M2655", "N1059" ]
N. J. A. Sloane
2025-04-24T18:38:56
oeisdata/seq/A000/A000225.seq
710f886bab7b802ca37d8221c81d2030
A000226
Number of n-node unlabeled connected graphs with one cycle of length 3.
[ "1", "1", "3", "7", "18", "44", "117", "299", "793", "2095", "5607", "15047", "40708", "110499", "301541", "825784", "2270211", "6260800", "17319689", "48042494", "133606943", "372430476", "1040426154", "2912415527", "8167992598", "22947778342", "64577555147", "182009003773", "513729375064", "1452007713130" ]
[ "nonn", "nice" ]
83
3
3
[ "A000081", "A000226", "A001429", "A033185", "A058879", "A217781" ]
[ "M2668", "N1066" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000226.seq
a5667fb1ad4f3419f74d65cc2c6e51eb
A000227
Nearest integer to e^n.
[ "1", "3", "7", "20", "55", "148", "403", "1097", "2981", "8103", "22026", "59874", "162755", "442413", "1202604", "3269017", "8886111", "24154953", "65659969", "178482301", "485165195", "1318815734", "3584912846", "9744803446", "26489122130", "72004899337", "195729609429", "532048240602", "1446257064291", "3931334297144", "10686474581524" ]
[ "nonn", "easy", "nice" ]
35
0
2
[ "A000149", "A000227", "A001671", "A002160" ]
[ "M2678", "N1071" ]
N. J. A. Sloane
2018-05-28T14:22:56
oeisdata/seq/A000/A000227.seq
6c736a2ef605e415f387125dd6b4a0f1
A000228
Number of hexagonal polyominoes (or hexagonal polyforms, or planar polyhexes) with n cells.
[ "1", "1", "3", "7", "22", "82", "333", "1448", "6572", "30490", "143552", "683101", "3274826", "15796897", "76581875", "372868101", "1822236628", "8934910362", "43939164263", "216651036012", "1070793308942", "5303855973849", "26323064063884", "130878392115834", "651812979669234", "3251215493161062", "16240020734253127", "81227147768301723", "406770970805865187", "2039375198751047333" ]
[ "nonn", "nice", "hard" ]
106
1
3
[ "A000105", "A000228", "A000577", "A001207", "A001998", "A002216", "A005963", "A006535", "A018190", "A030225", "A036359", "A057779", "A057973", "A103465", "A258019", "A258206", "A364306" ]
[ "M2682", "N1072" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000228.seq
9e176377c5bcab07ce1aede5bf9db0f4
A000229
a(n) is the least number m such that the n-th prime is the least quadratic nonresidue modulo m.
[ "3", "7", "23", "71", "311", "479", "1559", "5711", "10559", "18191", "31391", "422231", "701399", "366791", "3818929", "9257329", "22000801", "36415991", "48473881", "175244281", "120293879", "427733329", "131486759", "3389934071", "2929911599", "7979490791", "36504256799", "23616331489", "89206899239", "121560956039" ]
[ "nonn", "nice" ]
77
1
1
[ "A000229", "A002223", "A020649", "A025021", "A045535", "A053760", "A133435", "A307809" ]
[ "M2684", "N1074" ]
N. J. A. Sloane
2019-07-22T17:27:07
oeisdata/seq/A000/A000229.seq
374434c6bd96e8ddbee80674a1b03267
A000230
a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.
[ "2", "3", "7", "23", "89", "139", "199", "113", "1831", "523", "887", "1129", "1669", "2477", "2971", "4297", "5591", "1327", "9551", "30593", "19333", "16141", "15683", "81463", "28229", "31907", "19609", "35617", "82073", "44293", "43331", "34061", "89689", "162143", "134513", "173359", "31397", "404597", "212701", "188029", "542603", "265621", "461717", "155921", "544279", "404851", "927869", "1100977", "360653", "604073" ]
[ "nonn", "nice" ]
156
0
1
[ "A000230", "A001223", "A001632", "A002386", "A005250", "A038664", "A045881", "A100180", "A100964", "A133429", "A133430", "A226657", "A229021", "A229028", "A229030", "A229033", "A229034" ]
[ "M2685", "N1075" ]
N. J. A. Sloane
2025-02-12T14:21:33
oeisdata/seq/A000/A000230.seq
cb2a7c26854a4a036a9e9d1410eb57ca
A000231
Number of inequivalent Boolean functions of n variables under action of complementing group.
[ "2", "3", "7", "46", "4336", "134281216", "288230380379570176", "2658455991569831764110243006194384896", "452312848583266388373324160190187140390789016525312000869601987902398529536" ]
[ "easy", "nonn", "nice" ]
42
0
1
[ "A000231", "A051502", "A054724" ]
[ "M2702", "N1083" ]
N. J. A. Sloane
2023-01-27T12:13:20
oeisdata/seq/A000/A000231.seq
a756f1d54d74c054d27369b392b13199
A000232
Construct a triangle as in A036262. Sequence is one less than the position of the first number larger than 2 in the n-th row (n-th difference).
[ "3", "8", "14", "14", "25", "24", "23", "22", "25", "59", "98", "97", "98", "97", "174", "176", "176", "176", "176", "291", "290", "289", "740", "874", "873", "872", "873", "872", "871", "870", "869", "868", "867", "866", "2180", "2179", "2178", "2177", "2771", "2770", "2769", "2768", "2767", "2766", "2765", "2764", "2763", "2763", "2763", "2763", "3366", "4208", "4207" ]
[ "nonn" ]
36
1
1
[ "A000232", "A001549" ]
[ "M2718", "N1089" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000232.seq
5baa02afb3c962f89269b958d41ac04e
A000233
Generalized class numbers c_(n,1).
[ "1", "3", "8", "16", "30", "46", "64", "96", "126", "158", "216", "256", "302", "396", "448", "512", "636", "702", "792", "960", "1052", "1118", "1344", "1472", "1550", "1866", "1944", "2048", "2442", "2540", "2688", "3072", "3212", "3388", "3888", "4032", "4094", "4746", "4928", "5056", "5832", "5852", "5976", "6912", "7020", "7180", "8064", "8192" ]
[ "nonn", "easy" ]
41
1
2
[ "A000233", "A000362", "A000508" ]
[ "M2722", "N1090" ]
N. J. A. Sloane
2024-10-05T16:29:50
oeisdata/seq/A000/A000233.seq
5521992a025c39876abe6ad28c4348b6
A000234
Partitions into non-integral powers (see Comments for precise definition).
[ "1", "3", "8", "18", "37", "72", "136", "251", "445", "770", "1312", "2202", "3632", "5908", "9501", "15111", "23781", "37083", "57293", "87813", "133530", "201574", "302265", "450317", "666743", "981488", "1437003", "2092976", "3033253", "4375104", "6282026", "8981046", "12786327", "18131492", "25612628" ]
[ "nonn" ]
31
1
2
null
[ "M2730", "N1095" ]
N. J. A. Sloane
2017-10-02T02:12:54
oeisdata/seq/A000/A000234.seq
d9ddd3bf8bd0db675292662ed803bfe9
A000235
Number of n-node rooted trees of height 3.
[ "0", "0", "0", "1", "3", "8", "18", "38", "76", "147", "277", "509", "924", "1648", "2912", "5088", "8823", "15170", "25935", "44042", "74427", "125112", "209411", "348960", "579326", "958077", "1579098", "2593903", "4247768", "6935070", "11290627", "18330973", "29684082", "47946852", "77258764", "124198083" ]
[ "nonn" ]
41
1
5
[ "A000235", "A034781" ]
[ "M2732", "N1097" ]
N. J. A. Sloane
2018-02-09T21:43:13
oeisdata/seq/A000/A000235.seq
e6e12100030ff8046221710a88efcd7f
A000236
Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m).
[ "3", "8", "20", "44", "80", "343", "288", "608", "1023", "2848", "4095", "40959", "16383", "32768", "11375", "655360", "262143", "3670016", "1048575", "2097151" ]
[ "nonn", "more" ]
37
2
1
[ "A000236", "A000445", "A111931" ]
[ "M2737", "N1099" ]
N. J. A. Sloane
2017-10-19T10:48:40
oeisdata/seq/A000/A000236.seq
689eecdcaa99b971ebcec213f4b6353d
A000237
Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.
[ "0", "1", "1", "3", "8", "26", "84", "297", "1066", "3976", "15093", "58426", "229189", "910127", "3649165", "14756491", "60103220", "246357081", "1015406251", "4205873378", "17497745509", "73084575666", "306352303774", "1288328048865", "5433980577776", "22982025183983" ]
[ "nonn", "eigen", "nice", "easy" ]
27
0
4
[ "A000083", "A000237", "A000314", "A035082", "A035349", "A035357" ]
[ "M2754", "N1107" ]
N. J. A. Sloane
2018-08-30T18:56:58
oeisdata/seq/A000/A000237.seq
93d4c26545aa617e8429809da3968d57
A000238
Number of oriented trees with n nodes.
[ "1", "1", "3", "8", "27", "91", "350", "1376", "5743", "24635", "108968", "492180", "2266502", "10598452", "50235931", "240872654", "1166732814", "5702001435", "28088787314", "139354922608", "695808554300", "3494390057212", "17641695461662", "89495023510876", "456009893224285", "2332997330210440" ]
[ "nonn", "nice" ]
63
1
3
[ "A000060", "A000151", "A000238", "A051437", "A334827", "A335362" ]
[ "M2756", "N1108" ]
N. J. A. Sloane
2020-06-09T09:22:57
oeisdata/seq/A000/A000238.seq
ccd15bc6b11b33832b1dc3ed0e778e47
A000239
One-half of number of permutations of [n] with exactly one run of adjacent symbols differing by 1.
[ "1", "1", "3", "8", "28", "143", "933", "7150", "62310", "607445", "6545935", "77232740", "989893248", "13692587323", "203271723033", "3223180454138", "54362625941818", "971708196867905", "18347779304380995", "364911199401630640", "7624625589633857940", "166977535317365068775", "3824547112283439914893", "91440772473772839055238" ]
[ "nonn" ]
37
1
3
[ "A000239", "A010030" ]
[ "M2758", "N1109" ]
N. J. A. Sloane
2016-02-06T09:46:27
oeisdata/seq/A000/A000239.seq
51d5de079a06aa0e9d71a19a4ddf9fe8
A000240
Rencontres numbers: number of permutations of [n] with exactly one fixed point.
[ "1", "0", "3", "8", "45", "264", "1855", "14832", "133497", "1334960", "14684571", "176214840", "2290792933", "32071101048", "481066515735", "7697064251744", "130850092279665", "2355301661033952", "44750731559645107", "895014631192902120", "18795307255050944541", "413496759611120779880" ]
[ "nonn", "easy", "nice" ]
133
1
3
[ "A000166", "A000240", "A000387", "A000449", "A000475", "A008290", "A008291", "A129135", "A170942", "A180188" ]
[ "M2763", "N1111" ]
N. J. A. Sloane, Simon Plouffe
2025-01-05T19:51:31
oeisdata/seq/A000/A000240.seq
8d71a1591575bd784879f812c6639508
A000241
Crossing number of complete graph with n nodes.
[ "0", "0", "0", "0", "0", "1", "3", "9", "18", "36", "60", "100", "150", "225", "315" ]
[ "nonn", "more", "nice" ]
137
0
7
[ "A000241", "A007333", "A014540", "A028723", "A030179", "A121021", "A191928" ]
[ "M2772", "N1115" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000241.seq
d6f29b489bbee8b98f9f989749e9311c
A000242
3rd power of rooted tree enumerator; number of linear forests of 3 rooted trees.
[ "1", "3", "9", "25", "69", "186", "503", "1353", "3651", "9865", "26748", "72729", "198447", "543159", "1491402", "4107152", "11342826", "31408719", "87189987", "242603970", "676524372", "1890436117", "5292722721", "14845095153", "41708679697", "117372283086", "330795842217" ]
[ "nonn", "easy", "nice" ]
37
3
2
[ "A000081", "A000106", "A000242", "A000300", "A000343", "A000395", "A339067" ]
[ "M2798", "N1126" ]
N. J. A. Sloane
2021-01-03T04:30:19
oeisdata/seq/A000/A000242.seq
3c05473b1feb145ffe8f6c611c5fe051
A000243
Number of trees with n nodes, 2 of which are labeled.
[ "1", "3", "9", "26", "75", "214", "612", "1747", "4995", "14294", "40967", "117560", "337830", "972027", "2800210", "8075889", "23315775", "67380458", "194901273", "564239262", "1634763697", "4739866803", "13752309730", "39926751310", "115988095896", "337138003197" ]
[ "nonn", "easy", "nice" ]
46
2
2
[ "A000243", "A034799" ]
[ "M2803", "N1128" ]
N. J. A. Sloane
2023-03-23T23:09:28
oeisdata/seq/A000/A000243.seq
aba4ceff2727fef5d1585eddd54dbd0a
A000244
Powers of 3: a(n) = 3^n.
[ "1", "3", "9", "27", "81", "243", "729", "2187", "6561", "19683", "59049", "177147", "531441", "1594323", "4782969", "14348907", "43046721", "129140163", "387420489", "1162261467", "3486784401", "10460353203", "31381059609", "94143178827", "282429536481", "847288609443", "2541865828329", "7625597484987" ]
[ "nonn", "nice", "easy", "core" ]
529
0
2
[ "A000079", "A000244", "A001047", "A004094", "A004167", "A006521", "A008776", "A009964", "A014945", "A028243", "A028909", "A028910", "A035002", "A036447", "A046816", "A057615", "A058481", "A092477", "A100772", "A125076", "A153279", "A159991", "A163632", "A217764", "A263451", "A275414", "A321539", "A321540", "A321541", "A321542" ]
[ "M2807", "N1129" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000244.seq
18d3b86249400fba9e708efd1e5f0aab
A000245
a(n) = 3*(2*n)!/((n+2)!*(n-1)!).
[ "0", "1", "3", "9", "28", "90", "297", "1001", "3432", "11934", "41990", "149226", "534888", "1931540", "7020405", "25662825", "94287120", "347993910", "1289624490", "4796857230", "17902146600", "67016296620", "251577050010", "946844533674", "3572042254128", "13505406670700", "51166197843852", "194214400834356" ]
[ "nonn", "easy", "nice", "changed" ]
307
0
3
[ "A000108", "A000245", "A000344", "A000588", "A001392", "A001622", "A002057", "A003517", "A003518", "A003519", "A009766", "A014137", "A030237", "A033184", "A047072", "A059365", "A067323", "A099039", "A099364", "A106566", "A130020", "A154558" ]
[ "M2809", "N1130" ]
N. J. A. Sloane
2025-04-16T10:58:46
oeisdata/seq/A000/A000245.seq
a512b26bbfedede40a143e768dfafae4
A000246
Number of permutations in the symmetric group S_n that have odd order.
[ "1", "1", "1", "3", "9", "45", "225", "1575", "11025", "99225", "893025", "9823275", "108056025", "1404728325", "18261468225", "273922023375", "4108830350625", "69850115960625", "1187451971330625", "22561587455281875", "428670161650355625", "9002073394657468125", "189043541287806830625" ]
[ "nonn", "easy" ]
223
0
4
[ "A000246", "A001818", "A001900", "A002019", "A002867", "A049218", "A059838", "A079484", "A111594", "A262124", "A262125" ]
[ "M2824", "N1137" ]
N. J. A. Sloane
2025-02-10T11:17:55
oeisdata/seq/A000/A000246.seq
d0bca6d98f696bb703b9560778fa6fc9
A000247
a(n) = 2^n - n - 2.
[ "0", "3", "10", "25", "56", "119", "246", "501", "1012", "2035", "4082", "8177", "16368", "32751", "65518", "131053", "262124", "524267", "1048554", "2097129", "4194280", "8388583", "16777190", "33554405", "67108836", "134217699", "268435426", "536870881", "1073741792", "2147483615" ]
[ "nonn", "easy", "nice" ]
139
2
2
[ "A000247", "A000478", "A058844" ]
[ "M2836", "N1141" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000247.seq
564ab760f74d390830977d4f43deb946
A000248
Expansion of e.g.f. exp(x*exp(x)).
[ "1", "1", "3", "10", "41", "196", "1057", "6322", "41393", "293608", "2237921", "18210094", "157329097", "1436630092", "13810863809", "139305550066", "1469959371233", "16184586405328", "185504221191745", "2208841954063318", "27272621155678841", "348586218389733556", "4605223387997411873" ]
[ "easy", "nonn", "nice" ]
157
0
3
[ "A000248", "A005727", "A048993", "A098697", "A133399", "A210725", "A245501", "A279636" ]
[ "M2857", "N1148" ]
N. J. A. Sloane, Simon Plouffe
2023-02-20T09:07:20
oeisdata/seq/A000/A000248.seq
04aabff764b6110aa202fa61690a1e35
A000249
Nearest integer to modified Bessel function K_n(5).
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "3", "10", "42", "193", "966", "5215", "30170", "186234", "1222065", "8496274", "62395234", "482700052", "3923995651", "33444263516", "298233514595", "2777192597789", "26959282453367", "272370017131462", "2859607460620573", "31156130591833647", "351808270089157421" ]
[ "nonn" ]
32
0
10
null
[ "M2859", "N1150" ]
N. J. A. Sloane
2023-12-09T07:04:38
oeisdata/seq/A000/A000249.seq
9d31259c94febf673367480c0f417aa7
A000250
Number of symmetric reflexive relations on n nodes: (1/2)*A000666.
[ "1", "3", "10", "45", "272", "2548", "39632", "1104306", "56871880", "5463113568", "978181717680", "326167542296048", "202701136710498400", "235284321080559981952", "511531711735594715527360", "2089424601541011618029114896", "16084004145036771186002041099712", "234026948449058790311618594954430848", "6454432593140577452393525511509194184320" ]
[ "nonn", "nice" ]
30
1
2
[ "A000250", "A000595", "A001173", "A001174" ]
[ "M2868", "N1153" ]
N. J. A. Sloane
2024-07-15T10:22:56
oeisdata/seq/A000/A000250.seq
df62c03c619ee751526493e848e2074d
A000251
Number of trees of diameter 6.
[ "1", "3", "11", "29", "74", "167", "367", "755", "1515", "2931", "5551", "10263", "18677", "33409", "59024", "102984", "177915", "304458", "516939", "871180", "1458882", "2428548", "4021670", "6627515", "10874462", "17770474", "28932739", "46943967", "75925797", "122433291", "196879385", "315759282", "505168033", "806290796", "1284034606", "2040485004", "3235965074", "5121801962", "8091411114", "12759606939", "20085832527", "31565046053", "49523414558", "77575278933", "121329065354", "189475663960", "295465391518", "460087656595", "715436020515", "1110994054004" ]
[ "nonn" ]
31
7
2
[ "A000251", "A000550", "A034853" ]
[ "M2887", "N1158" ]
N. J. A. Sloane
2023-05-19T04:19:17
oeisdata/seq/A000/A000251.seq
074606d61a89c1fc3b5bbe494772e65f
A000252
Number of invertible 2 X 2 matrices mod n.
[ "1", "6", "48", "96", "480", "288", "2016", "1536", "3888", "2880", "13200", "4608", "26208", "12096", "23040", "24576", "78336", "23328", "123120", "46080", "96768", "79200", "267168", "73728", "300000", "157248", "314928", "193536", "682080", "138240", "892800", "393216", "633600", "470016", "967680", "373248", "1822176", "738720" ]
[ "nonn", "easy", "nice", "mult" ]
76
1
2
[ "A000056", "A000252", "A011785", "A011786", "A059238", "A064767", "A227499", "A305186", "A316566", "A316622" ]
null
N. J. A. Sloane
2025-03-04T18:05:56
oeisdata/seq/A000/A000252.seq
dc869bddf8403cafca593a6ab2ee0e66
A000253
a(n) = 2*a(n-1) - a(n-2) + a(n-3) + 2^(n-1).
[ "0", "1", "4", "11", "27", "63", "142", "312", "673", "1432", "3015", "6295", "13055", "26926", "55284", "113081", "230572", "468883", "951347", "1926527", "3894878", "7863152", "15855105", "31936240", "64269135", "129234351", "259690239", "521524126", "1046810092", "2100221753", "4212028452", "8444387067" ]
[ "nonn" ]
47
0
3
null
null
Jason Howald (jahowald(AT)umich.edu)
2022-08-12T20:01:55
oeisdata/seq/A000/A000253.seq
bb179e865f678d71bebfe7bceb45d6f5
A000254
Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) = (n+1)*a(n) + n!.
[ "0", "1", "3", "11", "50", "274", "1764", "13068", "109584", "1026576", "10628640", "120543840", "1486442880", "19802759040", "283465647360", "4339163001600", "70734282393600", "1223405590579200", "22376988058521600", "431565146817638400", "8752948036761600000", "186244810780170240000" ]
[ "nonn", "easy", "nice" ]
321
0
3
[ "A000254", "A000399", "A000454", "A000482", "A000774", "A001233", "A001234", "A004041", "A008275", "A008969", "A021009", "A024167", "A046674", "A049034", "A081048", "A081358", "A092691", "A094587", "A121633", "A136662", "A151881", "A243569", "A243570" ]
[ "M2902", "N1165" ]
N. J. A. Sloane
2024-04-15T13:05:04
oeisdata/seq/A000/A000254.seq
cf6e320a798968350908b47dd84cce82
A000255
a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.
[ "1", "1", "3", "11", "53", "309", "2119", "16687", "148329", "1468457", "16019531", "190899411", "2467007773", "34361893981", "513137616783", "8178130767479", "138547156531409", "2486151753313617", "47106033220679059", "939765362752547227", "19690321886243846661", "432292066866171724421" ]
[ "nonn", "easy", "nice" ]
317
0
3
[ "A000153", "A000166", "A000255", "A000261", "A001909", "A001910", "A002469", "A010027", "A046740", "A052655", "A055790", "A068106", "A086764", "A087982", "A087983", "A089475", "A089480", "A090010", "A090012", "A090013", "A090014", "A090015", "A090016", "A153869", "A159610" ]
[ "M2905", "N1166" ]
N. J. A. Sloane
2025-01-05T19:51:31
oeisdata/seq/A000/A000255.seq
e5243c42abad9764d4f8f310b12a7f76
A000256
Number of simple triangulations of the plane with n nodes.
[ "1", "1", "0", "1", "3", "12", "52", "241", "1173", "5929", "30880", "164796", "897380", "4970296", "27930828", "158935761", "914325657", "5310702819", "31110146416", "183634501753", "1091371140915", "6526333259312", "39246152584304", "237214507388796", "1440503185260748" ]
[ "nonn", "nice" ]
89
3
5
[ "A000256", "A210664" ]
[ "M2923", "N1173" ]
N. J. A. Sloane
2022-04-13T13:25:14
oeisdata/seq/A000/A000256.seq
12cf5b3218584c1a9ff8bfe8d6879783
A000257
Number of rooted bicubic maps: a(n) = (8*n-4)*a(n-1)/(n+2) for n >= 2, a(0) = a(1) = 1.
[ "1", "1", "3", "12", "56", "288", "1584", "9152", "54912", "339456", "2149888", "13891584", "91287552", "608583680", "4107939840", "28030648320", "193100021760", "1341536993280", "9390758952960", "66182491668480", "469294031831040", "3346270487838720", "23981605162844160", "172667557172477952" ]
[ "nonn", "easy", "nice" ]
229
0
3
[ "A000257", "A007054", "A069726", "A101477", "A298358" ]
[ "M2927", "N1175" ]
N. J. A. Sloane
2024-08-03T11:24:19
oeisdata/seq/A000/A000257.seq
1ed7a8533df7900dcf0fff12696062c8
A000258
Expansion of e.g.f. exp(exp(exp(x)-1)-1).
[ "1", "1", "3", "12", "60", "358", "2471", "19302", "167894", "1606137", "16733779", "188378402", "2276423485", "29367807524", "402577243425", "5840190914957", "89345001017415", "1436904211547895", "24227076487779802", "427187837301557598", "7859930038606521508", "150601795280158255827" ]
[ "nonn", "easy", "nice" ]
121
0
3
[ "A000110", "A000258", "A000307", "A000357", "A000405", "A001669", "A039811", "A130191", "A144150" ]
[ "M2932", "N1178" ]
N. J. A. Sloane
2023-10-27T18:22:23
oeisdata/seq/A000/A000258.seq
b0374af0876b606f39179bf5e60b32cd
A000259
Number of certain rooted planar maps.
[ "1", "3", "13", "63", "326", "1761", "9808", "55895", "324301", "1908878", "11369744", "68395917", "414927215", "2535523154", "15592255913", "96419104103", "599176447614", "3739845108057", "23435007764606", "147374772979438", "929790132901804", "5883377105975922", "37328490926964481", "237427707464042693" ]
[ "nonn" ]
62
1
2
[ "A000259", "A046651" ]
[ "M2943", "N1185" ]
N. J. A. Sloane
2024-10-24T12:33:55
oeisdata/seq/A000/A000259.seq
4a50b00793a7dc65a011cde67e349d84
A000260
Number of rooted simplicial 3-polytopes with n+3 nodes; or rooted 3-connected triangulations with 2n+2 faces; or rooted 3-connected trivalent maps with 2n+2 vertices.
[ "1", "1", "3", "13", "68", "399", "2530", "16965", "118668", "857956", "6369883", "48336171", "373537388", "2931682810", "23317105140", "187606350645", "1524813969276", "12504654858828", "103367824774012", "860593023907540", "7211115497448720", "60776550501588855" ]
[ "nonn", "nice", "easy" ]
232
0
3
[ "A000168", "A000256", "A000260", "A000309", "A000698", "A000699", "A002005", "A006013", "A027836", "A062980", "A069271", "A146305", "A255918", "A263191", "A267827", "A290326", "A341856", "A342981" ]
[ "M2946", "N1187" ]
N. J. A. Sloane
2023-10-25T09:31:10
oeisdata/seq/A000/A000260.seq
caa22b70c63d8679bb8e898319742a1d
A000261
a(n) = n*a(n-1) + (n-3)*a(n-2), with a(1) = 0, a(2) = 1.
[ "0", "1", "3", "13", "71", "465", "3539", "30637", "296967", "3184129", "37401155", "477471021", "6581134823", "97388068753", "1539794649171", "25902759280525", "461904032857319", "8702813980639617", "172743930157869827", "3602826440828270029", "78768746000235327495", "1801366114380914335441" ]
[ "nonn" ]
61
1
3
[ "A000153", "A000255", "A000261", "A001909", "A001910", "A055790", "A086764", "A090010", "A090012", "A090016" ]
[ "M2949", "N1189" ]
N. J. A. Sloane
2025-01-05T04:44:35
oeisdata/seq/A000/A000261.seq
8cf46472f4f7199089aa6d95986613c4
A000262
Number of "sets of lists": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset.
[ "1", "1", "3", "13", "73", "501", "4051", "37633", "394353", "4596553", "58941091", "824073141", "12470162233", "202976401213", "3535017524403", "65573803186921", "1290434218669921", "26846616451246353", "588633468315403843", "13564373693588558173", "327697927886085654441", "8281153039765859726341" ]
[ "nonn", "easy", "core", "nice" ]
488
0
3
[ "A000110", "A000262", "A001263", "A001700", "A002378", "A002720", "A002868", "A005408", "A008297", "A052852", "A056953", "A066668", "A082579", "A111596", "A132393", "A255807", "A255819", "A257740", "A271703", "A318976", "A319501" ]
[ "M2950", "N1190" ]
N. J. A. Sloane
2025-02-11T11:50:05
oeisdata/seq/A000/A000262.seq
c20061dd78cb75b9213d746250e83d24
A000263
Number of partitions into non-integral powers.
[ "3", "14", "39", "91", "173", "307", "502", "779", "1150", "1651", "2280", "3090", "4090", "5313", "6787", "8564", "10643", "13103", "15948", "19235", "23000", "27316", "32174", "37677", "43849", "50758", "58427", "66978", "76373", "86765", "98171", "110662", "124310", "139202", "155339", "172885" ]
[ "nonn" ]
20
3
1
null
[ "M2967", "N1200" ]
N. J. A. Sloane
2016-02-06T12:10:08
oeisdata/seq/A000/A000263.seq
38a03331b67d14b9e9cf2f2ca45d41a7
A000264
Number of 3-edge-connected rooted cubic maps with 2n nodes and a distinguished Hamiltonian cycle.
[ "1", "1", "3", "14", "80", "518", "3647", "27274", "213480", "1731652", "14455408", "123552488", "1077096124", "9548805240", "85884971043", "782242251522", "7203683481720", "66989439309452", "628399635777936", "5940930064989720", "56562734108608536" ]
[ "nonn", "nice" ]
31
1
3
[ "A000264", "A000309", "A000356", "A004304" ]
[ "M2974", "N1203" ]
N. J. A. Sloane
2019-01-01T06:34:05
oeisdata/seq/A000/A000264.seq
785a6467f72f79d6628a92ab672adb08
A000265
Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n.
[ "1", "1", "3", "1", "5", "3", "7", "1", "9", "5", "11", "3", "13", "7", "15", "1", "17", "9", "19", "5", "21", "11", "23", "3", "25", "13", "27", "7", "29", "15", "31", "1", "33", "17", "35", "9", "37", "19", "39", "5", "41", "21", "43", "11", "45", "23", "47", "3", "49", "25", "51", "13", "53", "27", "55", "7", "57", "29", "59", "15", "61", "31", "63", "1", "65", "33", "67", "17", "69", "35", "71", "9", "73", "37", "75", "19", "77" ]
[ "mult", "nonn", "easy", "nice" ]
394
1
3
[ "A000004", "A000010", "A000123", "A000217", "A000225", "A000265", "A001227", "A001511", "A003602", "A003961", "A006516", "A006519", "A007814", "A008683", "A014577", "A020988", "A025480", "A026741", "A027750", "A035263", "A038502", "A038550", "A049606", "A064989", "A065330", "A068563", "A069834", "A075101", "A099545", "A111918", "A111919", "A111920", "A111921", "A111922", "A111923", "A111929", "A111930", "A125650", "A127793", "A132739", "A132740", "A135013", "A156769", "A160469", "A182469", "A195056", "A209308", "A213671", "A220466", "A236999", "A242603", "A326937" ]
[ "M2222", "N0881" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000265.seq
51e279d71f159f0b46aa2ef3ae7a66cd
A000266
Expansion of e.g.f. exp(-x^2/2) / (1-x).
[ "1", "1", "1", "3", "15", "75", "435", "3045", "24465", "220185", "2200905", "24209955", "290529855", "3776888115", "52876298475", "793144477125", "12690313661025", "215735332237425", "3883235945814225", "73781482970470275", "1475629660064134575", "30988222861346826075", "681740902935880863075" ]
[ "nonn" ]
75
0
4
[ "A000090", "A000138", "A000266", "A027616", "A130905", "A193385" ]
[ "M2991", "N1211" ]
N. J. A. Sloane
2022-08-06T07:25:17
oeisdata/seq/A000/A000266.seq
ad8f1bceaf4b105f540464a33dc78b01
A000267
Integer part of square root of 4n+1.
[ "1", "2", "3", "3", "4", "4", "5", "5", "5", "6", "6", "6", "7", "7", "7", "7", "8", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17" ]
[ "nonn", "easy", "nice", "tabf" ]
97
0
2
[ "A000196", "A000267", "A002620", "A016813", "A055086", "A070939", "A080037", "A094727", "A227368", "A240025" ]
null
N. J. A. Sloane
2024-11-24T01:49:31
oeisdata/seq/A000/A000267.seq
c7df03cd96822b51f47ada0675918c15
A000268
E.g.f.: -log(1+log(1+log(1-x))).
[ "1", "3", "15", "105", "947", "10472", "137337", "2085605", "36017472", "697407850", "14969626900", "352877606716", "9064191508018", "252024567201300", "7542036496650006", "241721880399970938", "8261159383595659128", "299916384730043070880", "11526945327529620432872", "467583770376898192016104" ]
[ "nonn" ]
45
1
2
[ "A000268", "A000310", "A000359", "A000406", "A001765", "A003713", "A039815" ]
[ "M3003", "N1218" ]
N. J. A. Sloane
2022-02-11T08:14:19
oeisdata/seq/A000/A000268.seq
e1ef67a278a1e963e857b2c2c36b5e58
A000269
Number of trees with n nodes, 3 of which are labeled.
[ "3", "16", "67", "251", "888", "3023", "10038", "32722", "105228", "334836", "1056611", "3311784", "10322791", "32026810", "98974177", "304835956", "936147219", "2867586542", "8764280567", "26733395986", "81399821915", "247459136331", "751211286356", "2277496842016" ]
[ "nonn", "easy", "nice" ]
32
3
1
[ "A000269", "A034799" ]
[ "M3014", "N1220" ]
N. J. A. Sloane
2023-03-23T23:09:23
oeisdata/seq/A000/A000269.seq
11afc0885902f03774067d316860d400
A000270
For n >= 2, a(n) = b(n+1)+b(n)+b(n-1), where the b(i) are the ménage numbers A000179; a(0)=a(1)=1.
[ "1", "1", "0", "3", "16", "95", "672", "5397", "48704", "487917", "5373920", "64547175", "839703696", "11762247419", "176509466560", "2825125339305", "48040633506048", "864932233294681", "16436901752820288", "328791893988472843", "6905593482159150480", "151941269284478380119", "3495011687269591273312" ]
[ "nonn", "nice" ]
107
0
4
[ "A000179", "A000270", "A335391" ]
[ "M3019", "N1221" ]
N. J. A. Sloane
2024-12-10T12:30:57
oeisdata/seq/A000/A000270.seq
57a6a5c2493e8a7ee783637e535eda66
A000271
Sums of ménage numbers.
[ "1", "0", "0", "1", "3", "16", "96", "675", "5413", "48800", "488592", "5379333", "64595975", "840192288", "11767626752", "176574062535", "2825965531593", "48052401132800", "865108807357216", "16439727718351881", "328839946389605643", "6906458590966507696" ]
[ "nonn", "easy", "nice" ]
123
0
5
[ "A000179", "A000271", "A000904", "A001883", "A058057", "A137886", "A292574" ]
[ "M3020", "N1222" ]
N. J. A. Sloane
2022-09-08T08:44:27
oeisdata/seq/A000/A000271.seq
2e76e4fb60b0912c32cdd9f8e6342007
A000272
Number of trees on n labeled nodes: n^(n-2) with a(0)=1.
[ "1", "1", "1", "3", "16", "125", "1296", "16807", "262144", "4782969", "100000000", "2357947691", "61917364224", "1792160394037", "56693912375296", "1946195068359375", "72057594037927936", "2862423051509815793", "121439531096594251776", "5480386857784802185939" ]
[ "easy", "nonn", "core", "nice" ]
309
0
4
[ "A000055", "A000169", "A000254", "A000272", "A000312", "A007778", "A007830", "A008785", "A008791", "A033842", "A036361", "A036362", "A036506", "A052750", "A054581", "A058127", "A081048", "A083483", "A097170", "A105599", "A239910" ]
[ "M3027", "N1227" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000272.seq
3a708353904b451208d794910afa7007
A000273
Number of unlabeled simple digraphs with n nodes.
[ "1", "1", "3", "16", "218", "9608", "1540944", "882033440", "1793359192848", "13027956824399552", "341260431952972580352", "32522909385055886111197440", "11366745430825400574433894004224", "14669085692712929869037096075316220928", "70315656615234999521385506555979904091217920" ]
[ "nonn", "core", "nice" ]
119
0
3
[ "A000273", "A052283", "A217654" ]
[ "M3032", "N1229" ]
N. J. A. Sloane
2024-07-05T16:13:01
oeisdata/seq/A000/A000273.seq
2d887d199954e70752836e6e9fe1cdd3
A000274
Number of permutations of length n with 2 consecutive ascending pairs.
[ "0", "0", "1", "3", "18", "110", "795", "6489", "59332", "600732", "6674805", "80765135", "1057289046", "14890154058", "224497707343", "3607998868005", "61576514013960", "1112225784377144", "21197714949305577", "425131949816628507", "8950146311929021210", "197350726178034917670", "4548464355722328578691" ]
[ "easy", "nonn" ]
43
1
4
[ "A000166", "A000255", "A000274", "A000313", "A001260", "A001261", "A010027", "A046739", "A145886", "A145887" ]
[ "M3048", "N1236" ]
N. J. A. Sloane, Simon Plouffe
2024-11-26T07:01:30
oeisdata/seq/A000/A000274.seq
d0d2e35bcfa1bc3ac0cb39c7bb8bdf4a
A000275
Coefficients of a Bessel function (reciprocal of J_0(z)); also pairs of permutations with rise/rise forbidden.
[ "1", "1", "3", "19", "211", "3651", "90921", "3081513", "136407699", "7642177651", "528579161353", "44237263696473", "4405990782649369", "515018848029036937", "69818743428262376523", "10865441556038181291819", "1923889742567310611949459", "384565973956329859109177427", "86180438505835750284241676121" ]
[ "nonn", "nice" ]
99
0
3
[ "A000275", "A055133", "A115368", "A192721", "A212855", "A340986" ]
[ "M3065", "N1242" ]
N. J. A. Sloane
2024-05-04T10:18:01
oeisdata/seq/A000/A000275.seq
9bf84db978c98e4daea8229a8c5d1445
A000276
Associated Stirling numbers.
[ "3", "20", "130", "924", "7308", "64224", "623376", "6636960", "76998240", "967524480", "13096736640", "190060335360", "2944310342400", "48503818137600", "846795372595200", "15618926924697600", "303517672703078400", "6198400928176128000", "132720966600284160000", "2973385109386137600000" ]
[ "nonn" ]
52
4
1
[ "A000276", "A008306", "A052518", "A052881", "A259456" ]
[ "M3075", "N1248" ]
N. J. A. Sloane
2016-09-25T04:37:26
oeisdata/seq/A000/A000276.seq
190323eaf10a402643beab57977d7e86
A000277
3*n - 2*floor(sqrt(4*n+5)) + 5.
[ "1", "2", "5", "6", "9", "10", "13", "16", "17", "20", "23", "24", "27", "30", "33", "34", "37", "40", "43", "44", "47", "50", "53", "56", "57", "60", "63", "66", "69", "70", "73", "76", "79", "82", "85", "86", "89", "92", "95", "98", "101", "102", "105", "108", "111", "114", "117", "120", "121", "124", "127", "130", "133", "136", "139", "140", "143", "146", "149", "152", "155" ]
[ "nonn", "easy" ]
11
0
2
null
null
N. J. A. Sloane, based on a message from Michael S. Cann Jr. (mscannjr(AT)gmail.com)
2012-06-19T19:06:42
oeisdata/seq/A000/A000277.seq
22cb9a6021b1b858a1314dfb371bf4d3
A000278
a(n) = a(n-1) + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
[ "0", "1", "1", "2", "3", "7", "16", "65", "321", "4546", "107587", "20773703", "11595736272", "431558332068481", "134461531248108526465", "186242594112190847520182173826", "18079903385772308300945867582153787570051", "34686303861638264961101080464895364211215702792496667048327" ]
[ "nonn" ]
56
0
4
[ "A000278", "A000283", "A058182" ]
null
Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)
2023-01-05T03:54:38
oeisdata/seq/A000/A000278.seq
4a14d258d9a384fa3a5ae747c43b724c
A000279
Card matching: coefficients B[n,1] of t in the reduced hit polynomial A[n,n,n](t).
[ "3", "24", "216", "1824", "15150", "124416", "1014888", "8241792", "66724398", "538990800", "4346692680", "35009591040", "281699380560", "2264868936960", "18198009147600", "146142982814208", "1173123636533454", "9413509300965936", "75513633110271264", "605598295606296000", "4855626127979443908", "38924245740546950784" ]
[ "nonn" ]
46
1
1
[ "A000279", "A000489", "A000535", "A033581" ]
[ "M3106", "N1258" ]
N. J. A. Sloane
2015-09-23T20:34:56
oeisdata/seq/A000/A000279.seq
cf7cadc3f79e2f3af52148656e7400f2
A000280
a(n) = a(n-1) + a(n-2)^3.
[ "0", "1", "1", "2", "3", "11", "38", "1369", "56241", "2565782650", "177895665388171", "16891164530321501264425013171", "5629840598310484749297545401724540333537382" ]
[ "nonn" ]
25
0
4
[ "A000278", "A000280" ]
null
Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)
2017-01-31T01:28:00
oeisdata/seq/A000/A000280.seq
16ecc5ad8a38c826d39ec3db34f7ee51
A000281
Expansion of cos(x)/cos(2x).
[ "1", "3", "57", "2763", "250737", "36581523", "7828053417", "2309644635483", "898621108880097", "445777636063460643", "274613643571568682777", "205676334188681975553003", "184053312545818735778213457", "193944394596325636374396208563" ]
[ "nonn", "easy", "nice" ]
88
0
2
[ "A000281", "A000364", "A000825", "A001586", "A002437", "A064069", "A086646", "A093954", "A098432", "A188458", "A212435", "A235605", "A255883" ]
[ "M3163", "N1281" ]
N. J. A. Sloane
2019-11-11T10:23:58
oeisdata/seq/A000/A000281.seq
0a61c9f21483ee4b98f508ac75bf9f0a
A000282
Finite automata.
[ "3", "70", "3783", "338475", "40565585", "6061961733", "1083852977811", "225615988054171", "53595807366038234", "14308700593468127485", "4241390625289880226714", "1382214286200071777573643", "491197439886557439295166226", "189044982636675290371386547592", "78334771617452038208125184627931", "34771576300926271400714044414858372" ]
[ "nonn" ]
43
1
1
[ "A000282", "A002854", "A054732", "A054747" ]
[ "M3169", "N1285" ]
N. J. A. Sloane
2021-03-08T22:29:17
oeisdata/seq/A000/A000282.seq
61e068829658d1de28983241085b4ca8
A000283
a(n) = a(n-1)^2 + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
[ "0", "1", "1", "2", "5", "29", "866", "750797", "563696885165", "317754178345286893212434", "100967717855888389973004846476977145423449281581" ]
[ "nonn", "easy" ]
58
0
4
[ "A000278", "A000283" ]
null
Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)
2023-09-16T03:34:35
oeisdata/seq/A000/A000283.seq
3c260a1ea927697a0ee55689888f329d
A000284
a(n) = a(n-1)^3 + a(n-2) with a(0)=0, a(1)=1.
[ "0", "1", "1", "2", "9", "731", "390617900", "59601394712394173339000731", "211723599072542785377729319366442939995427829921816290889198752331804918235791" ]
[ "nonn", "easy" ]
30
0
4
[ "A000284", "A058182" ]
null
Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)
2020-05-08T17:39:57
oeisdata/seq/A000/A000284.seq
fd82d3e56d17648f626d8ec88a9a1e87
A000285
a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2.
[ "1", "4", "5", "9", "14", "23", "37", "60", "97", "157", "254", "411", "665", "1076", "1741", "2817", "4558", "7375", "11933", "19308", "31241", "50549", "81790", "132339", "214129", "346468", "560597", "907065", "1467662", "2374727", "3842389", "6217116", "10059505", "16276621", "26336126", "42612747", "68948873", "111561620", "180510493", "292072113", "472582606" ]
[ "nonn", "easy", "nice" ]
201
0
2
[ "A000285", "A013655", "A090888", "A091157", "A101220", "A104449", "A109754", "A131775" ]
[ "M3246", "N1309" ]
N. J. A. Sloane
2025-01-05T19:51:31
oeisdata/seq/A000/A000285.seq
227034b5641d382ccda749a15877d681
A000286
Number of positive integers <= 2^n of form 2 x^2 + 5 y^2.
[ "0", "1", "1", "4", "5", "11", "20", "36", "65", "119", "218", "412", "770", "1466", "2784", "5322", "10226", "19691", "38048", "73665", "142927", "277822", "540851", "1054502", "2058507", "4023164", "7871226", "15414517", "30213010", "59266164", "116343183", "228545303", "449240025", "883569304", "1738768584", "3423466797", "6743729031" ]
[ "nonn" ]
18
0
4
null
[ "M3251", "N1312" ]
N. J. A. Sloane
2017-10-17T05:52:26
oeisdata/seq/A000/A000286.seq
f80c0a09a83adaf4f37c402b5ffe2d5a
A000287
Number of rooted polyhedral graphs with n edges.
[ "1", "0", "4", "6", "24", "66", "214", "676", "2209", "7296", "24460", "82926", "284068", "981882", "3421318", "12007554", "42416488", "150718770", "538421590", "1932856590", "6969847486", "25237057110", "91729488354", "334589415276", "1224445617889", "4494622119424" ]
[ "nonn", "nice" ]
94
6
3
[ "A000256", "A000287" ]
[ "M3290", "N1326" ]
N. J. A. Sloane, Simon Plouffe
2024-09-25T11:24:09
oeisdata/seq/A000/A000287.seq
872b519f9d6b9de26bbedaf51e5fdc2f
A000288
Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.
[ "1", "1", "1", "1", "4", "7", "13", "25", "49", "94", "181", "349", "673", "1297", "2500", "4819", "9289", "17905", "34513", "66526", "128233", "247177", "476449", "918385", "1770244", "3412255", "6577333", "12678217", "24438049", "47105854", "90799453", "175021573", "337364929", "650291809", "1253477764" ]
[ "nonn", "easy" ]
109
0
5
[ "A000078", "A000288", "A060455" ]
[ "M3307", "N1332" ]
N. J. A. Sloane
2025-01-05T19:51:31
oeisdata/seq/A000/A000288.seq
fe22d1dcd8f3ec5d5053552bba9ca43a
A000289
A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1).
[ "1", "4", "7", "31", "871", "756031", "571580604871", "326704387862983487112031", "106735757048926752040856495274871386126283608871", "11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068031" ]
[ "nonn", "easy" ]
56
0
2
[ "A000058", "A000289" ]
[ "M3316", "N1333" ]
N. J. A. Sloane
2025-01-09T08:01:07
oeisdata/seq/A000/A000289.seq
5c098cc7632ff68f0297fb4bb217b5ce
A000290
The squares: a(n) = n^2.
[ "0", "1", "4", "9", "16", "25", "36", "49", "64", "81", "100", "121", "144", "169", "196", "225", "256", "289", "324", "361", "400", "441", "484", "529", "576", "625", "676", "729", "784", "841", "900", "961", "1024", "1089", "1156", "1225", "1296", "1369", "1444", "1521", "1600", "1681", "1764", "1849", "1936", "2025", "2116", "2209", "2304", "2401", "2500" ]
[ "nonn", "core", "easy", "nice", "mult" ]
826
0
3
[ "A000290", "A000447", "A000697", "A000745", "A001105", "A001157", "A001788", "A002522", "A002577", "A004159", "A005408", "A005563", "A008865", "A013661", "A028338", "A056944", "A059100", "A092205", "A095794", "A128200", "A128201", "A132191", "A143051", "A143470", "A143595", "A159918", "A162395", "A173277", "A186646", "A228039", "A342819" ]
[ "M3356", "N1350" ]
N. J. A. Sloane
2025-03-14T21:31:41
oeisdata/seq/A000/A000290.seq
c2fa09e59e4314445343262c9364f19f
A000291
Number of bipartite partitions of n white objects and 2 black ones.
[ "2", "4", "9", "16", "29", "47", "77", "118", "181", "267", "392", "560", "797", "1111", "1541", "2106", "2863", "3846", "5142", "6808", "8973", "11733", "15275", "19753", "25443", "32582", "41569", "52770", "66757", "84078", "105555", "131995", "164566", "204450", "253292", "312799", "385285", "473183", "579722", "708353", "863553" ]
[ "nonn" ]
69
0
1
[ "A000291", "A005380", "A054225" ]
[ "M1168", "N0447" ]
N. J. A. Sloane
2024-01-01T08:00:55
oeisdata/seq/A000/A000291.seq
f061d43c899a06165670f307ba9aacde
A000292
Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.
[ "0", "1", "4", "10", "20", "35", "56", "84", "120", "165", "220", "286", "364", "455", "560", "680", "816", "969", "1140", "1330", "1540", "1771", "2024", "2300", "2600", "2925", "3276", "3654", "4060", "4495", "4960", "5456", "5984", "6545", "7140", "7770", "8436", "9139", "9880", "10660", "11480", "12341", "13244", "14190", "15180" ]
[ "nonn", "core", "easy", "nice", "changed" ]
1,005
0
3
[ "A000217", "A000290", "A000292", "A000330", "A000332", "A000447", "A000578", "A001044", "A002492", "A002623", "A002817", "A005900", "A006527", "A006564", "A006566", "A007318", "A007814", "A014125", "A025035", "A040977", "A058187", "A060446", "A061552", "A068980", "A085691", "A094415", "A099174", "A100440", "A104712", "A122046", "A122047", "A122432", "A127324", "A133111", "A133112", "A145397", "A152205", "A156925", "A157703", "A158823", "A173964", "A175724", "A181118", "A190717", "A190718", "A216499", "A222716", "A231303", "A237616", "A275019", "A302695", "A321791", "A325000", "A327084", "A327085" ]
[ "M3382", "N1363" ]
N. J. A. Sloane
2025-04-16T03:03:15
oeisdata/seq/A000/A000292.seq
4e34a2da9585a7dd2d3d60216d1ecb21
A000293
a(n) = number of solid (i.e., three-dimensional) partitions of n.
[ "1", "1", "4", "10", "26", "59", "140", "307", "684", "1464", "3122", "6500", "13426", "27248", "54804", "108802", "214071", "416849", "805124", "1541637", "2930329", "5528733", "10362312", "19295226", "35713454", "65715094", "120256653", "218893580", "396418699", "714399381", "1281403841", "2287986987", "4067428375", "7200210523", "12693890803", "22290727268", "38993410516", "67959010130", "118016656268", "204233654229", "352245710866", "605538866862", "1037668522922", "1772700955975", "3019333854177", "5127694484375", "8683676638832", "14665233966068", "24700752691832", "41495176877972", "69531305679518" ]
[ "nonn", "nice" ]
102
0
3
[ "A000041", "A000219", "A000293", "A000294", "A000334", "A000390", "A000416", "A000427", "A001970", "A002835", "A002836", "A002974", "A003293", "A005980", "A007326", "A007713", "A037452", "A080207", "A114736", "A117433", "A161564", "A179855", "A323657" ]
[ "M3392", "N1371" ]
N. J. A. Sloane
2025-02-16T08:32:20
oeisdata/seq/A000/A000293.seq
0845c7bbbcea60538ca3076edee8b6a1
A000294
Expansion of g.f. Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2).
[ "1", "1", "4", "10", "26", "59", "141", "310", "692", "1483", "3162", "6583", "13602", "27613", "55579", "110445", "217554", "424148", "820294", "1572647", "2992892", "5652954", "10605608", "19765082", "36609945", "67405569", "123412204", "224728451", "407119735", "733878402", "1316631730", "2351322765", "4180714647", "7401898452", "13051476707", "22922301583", "40105025130", "69909106888", "121427077241", "210179991927", "362583131144" ]
[ "nonn", "easy" ]
125
0
3
[ "A000041", "A000219", "A000293", "A000294", "A000335", "A000391", "A000417", "A000428", "A007294", "A007326", "A028377", "A255939", "A255965", "A278403" ]
[ "M3393", "N1372" ]
N. J. A. Sloane
2023-02-16T12:23:58
oeisdata/seq/A000/A000294.seq
2b858889da0c57f67b027d171543146f
A000295
Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018).
[ "0", "0", "1", "4", "11", "26", "57", "120", "247", "502", "1013", "2036", "4083", "8178", "16369", "32752", "65519", "131054", "262125", "524268", "1048555", "2097130", "4194281", "8388584", "16777191", "33554406", "67108837", "134217700", "268435427", "536870882", "1073741793", "2147483616", "4294967263", "8589934558" ]
[ "nonn", "easy", "nice" ]
548
0
4
[ "A000079", "A000108", "A000217", "A000225", "A000295", "A000325", "A000975", "A001511", "A002662", "A002663", "A002664", "A007814", "A008292", "A008949", "A014473", "A014741", "A016031", "A028366", "A035039", "A035040", "A035041", "A035042", "A079583", "A107907", "A112493", "A112500", "A124324", "A125128", "A130103", "A130128", "A130321", "A130330", "A131768", "A131816", "A143291", "A173018" ]
[ "M3416", "N1382" ]
N. J. A. Sloane
2025-04-13T16:34:46
oeisdata/seq/A000/A000295.seq
c8b4fcd1a41eb71cac82a64a0cc47ede
A000296
Set partitions without singletons: number of partitions of an n-set into blocks of size > 1. Also number of cyclically spaced (or feasible) partitions.
[ "1", "0", "1", "1", "4", "11", "41", "162", "715", "3425", "17722", "98253", "580317", "3633280", "24011157", "166888165", "1216070380", "9264071767", "73600798037", "608476008122", "5224266196935", "46499892038437", "428369924118314", "4078345814329009", "40073660040755337", "405885209254049952", "4232705122975949401" ]
[ "nonn", "easy", "nice" ]
341
0
5
[ "A000110", "A000126", "A000296", "A001610", "A005493", "A006505", "A008299", "A057814", "A057837", "A066982", "A105794", "A106436", "A124323", "A169985", "A178866", "A216963", "A240936", "A261137", "A261139" ]
[ "M3423", "N1387" ]
N. J. A. Sloane
2025-01-05T19:51:31
oeisdata/seq/A000/A000296.seq
9aef1b7df3a87cec79177c0ee91cd0fa
A000297
a(n) = (n+1)*(n+3)*(n+8)/6.
[ "0", "4", "12", "25", "44", "70", "104", "147", "200", "264", "340", "429", "532", "650", "784", "935", "1104", "1292", "1500", "1729", "1980", "2254", "2552", "2875", "3224", "3600", "4004", "4437", "4900", "5394", "5920", "6479", "7072", "7700", "8364", "9065", "9804", "10582", "11400", "12259", "13160", "14104", "15092", "16125", "17204" ]
[ "nonn", "easy" ]
108
-1
2
[ "A000292", "A000297" ]
[ "M3434", "N1393" ]
N. J. A. Sloane
2025-01-05T19:51:31
oeisdata/seq/A000/A000297.seq
521781999d537785a52dfaadb7c55a3f
A000298
Number of partitions into non-integral powers.
[ "1", "4", "12", "30", "70", "159", "339", "706", "1436", "2853", "5551", "10622", "19975", "37043", "67811", "122561", "219090", "387578", "678977", "1178769", "2029115", "3465056", "5872648", "9882301", "16517284", "27430358", "45275673", "74297072", "121245153", "196810381", "317850809", "510830685", "817139589", "1301251186", "2063204707", "3257690903", "5123047561" ]
[ "nonn" ]
20
1
2
null
[ "M3439", "N1395" ]
N. J. A. Sloane
2015-06-27T17:55:46
oeisdata/seq/A000/A000298.seq
ee41a32e3d9aa4da705cbaf75d98c2f5
A000299
Number of n-node rooted trees of height 4.
[ "0", "0", "0", "0", "1", "4", "13", "36", "93", "225", "528", "1198", "2666", "5815", "12517", "26587", "55933", "116564", "241151", "495417", "1011950", "2055892", "4157514", "8371318", "16792066", "33564256", "66875221", "132849983", "263192599", "520087551", "1025295487", "2016745784", "3958608430", "7754810743" ]
[ "nonn" ]
42
1
6
[ "A000299", "A034781" ]
[ "M3461", "N1408" ]
N. J. A. Sloane
2018-02-09T21:43:19
oeisdata/seq/A000/A000299.seq
623dbe286a323f05803d1d9da2873fb8
A000300
4th power of rooted tree enumerator: linear forests of 4 rooted trees.
[ "1", "4", "14", "44", "133", "388", "1116", "3168", "8938", "25100", "70334", "196824", "550656", "1540832", "4314190", "12089368", "33911543", "95228760", "267727154", "753579420", "2123637318", "5991571428", "16923929406", "47857425416", "135478757308", "383929643780", "1089118243128", "3092612497260" ]
[ "nonn" ]
35
4
2
[ "A000081", "A000106", "A000242", "A000300", "A000343", "A000395", "A339067" ]
[ "M3479", "N1414" ]
N. J. A. Sloane
2021-01-03T04:30:43
oeisdata/seq/A000/A000300.seq
d57e6c1afc9000a9f86a440efe52c549