Datasets:
christopher
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oeis

Dataset card Data Studio Files
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666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
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A007201
Number of self-avoiding walks on hexagonal lattice.
[ "24", "84", "264", "1128", "4728", "20304", "86496", "369732", "1573608", "6703068", "28474704", "120922272", "512524704", "2171836752", "9190071984", "38866395264", "164191075824", "693230730864" ]
[ "nonn", "walk" ]
16
3
1
[ "A007200", "A007201" ]
[ "M5146" ]
Simon Plouffe
2017-11-20T13:58:37
oeisdata/seq/A007/A007201.seq
f0a69074432677ea291f5979656a0b42
A007202
Crystal ball sequence for hexagonal close-packing.
[ "1", "13", "57", "153", "323", "587", "967", "1483", "2157", "3009", "4061", "5333", "6847", "8623", "10683", "13047", "15737", "18773", "22177", "25969", "30171", "34803", "39887", "45443", "51493", "58057", "65157", "72813", "81047", "89879", "99331", "109423", "120177", "131613", "143753", "156617" ]
[ "nonn", "easy", "nice" ]
57
0
2
[ "A001845", "A005893", "A005894", "A005897", "A005898", "A005899", "A005901", "A005902", "A007202", "A007899", "A008137", "A010001", "A063489", "A299254", "A299255", "A299256", "A299257", "A299258", "A299259", "A299260", "A299261", "A299262", "A299263", "A299264", "A299265", "A299266", "A299267", "A299268", "A299269", "A299272", "A299273", "A299274", "A299275", "A299276", "A299277", "A299278", "A299279", "A299280", "A299281", "A299282", "A299283", "A299284", "A299285", "A299286", "A299287", "A299288", "A299289", "A299290", "A299291", "A299292" ]
[ "M4899" ]
N. J. A. Sloane and J. H. Conway
2024-03-14T23:25:59
oeisdata/seq/A007/A007202.seq
4ed6476e470496e02e4bcfbd70a8e511
A007203
Number of elements (a b / c d) in GL(2,Z) with |det| = 1, trace n and 0 <= a <= {b, c} <= d.
[ "1", "1", "2", "4", "3", "7", "4", "8", "6", "12", "5", "14", "7", "13", "13", "20", "5", "20", "10", "24", "14", "22", "12", "28", "18", "30", "14", "22", "17", "48", "12", "28", "19", "43", "19", "42", "25", "32", "23", "60", "18", "44", "28", "36", "33", "38", "24", "80", "18", "60", "39", "46", "18", "58", "36", "72", "29", "68", "28", "76", "37", "64", "34", "64", "61", "72", "25", "56", "34", "108" ]
[ "nonn" ]
5
1
3
[ "A006546", "A007104", "A007203", "A007295" ]
null
John Lewis (frc.mass.edu)
2020-01-01T16:57:26
oeisdata/seq/A007/A007203.seq
342b091ccf109e97ca93e8f29a2aea8e
A007204
Crystal ball sequence for D_4 lattice.
[ "1", "25", "169", "625", "1681", "3721", "7225", "12769", "21025", "32761", "48841", "70225", "97969", "133225", "177241", "231361", "297025", "375769", "469225", "579121", "707281", "855625", "1026169", "1221025", "1442401", "1692601", "1974025", "2289169", "2640625", "3031081", "3463321", "3940225", "4464769", "5040025" ]
[ "nonn", "easy", "nice" ]
100
0
2
[ "A000290", "A000583", "A001844", "A005563", "A007204", "A016754", "A057769", "A060300", "A069074", "A099761" ]
[ "M5182" ]
N. J. A. Sloane and J. H. Conway, Apr 28 1994
2024-02-15T04:41:01
oeisdata/seq/A007/A007204.seq
405e773097a3e47b86671894418fa29f
A007205
Erroneous version of A008349.
[ "1", "241", "9361", "120161" ]
[ "dead" ]
4
0
2
null
null
null
1999-12-11T03:00:00
oeisdata/seq/A007/A007205.seq
14220bd0f0fb17e66ab8ca17da96885a
A007206
Magnetization for honeycomb lattice.
[ "1", "0", "0", "-2", "-6", "-18", "-54", "-168", "-534", "-1732", "-5706", "-19038", "-64176", "-218190", "-747180", "-2574488", "-8918070", "-31036560", "-108457488", "-380390574", "-1338495492", "-4723664566", "-16714545822", "-59286878556", "-210755970528", "-750721297056", "-2679075662922", "-9577156141654", "-34290858526926", "-122959225609518" ]
[ "sign", "easy" ]
18
0
4
[ "A002928", "A007206", "A007207" ]
[ "M4124" ]
Simon Plouffe
2024-04-27T14:49:46
oeisdata/seq/A007/A007206.seq
b4edea786cebd609369b646786e47f86
A007207
Magnetization for hexagonal lattice.
[ "1", "0", "0", "-2", "0", "-12", "2", "-78", "24", "-548", "228", "-4050", "2030", "-30960", "17670", "-242402", "152520", "-1932000", "1312844", "-15612150", "11297052", "-127551884", "97291026", "-1051478274", "838994486", "-8732657724", "7246304736", "-72983051674", "62686156026", "-613243234224", "543146222970" ]
[ "sign", "easy" ]
21
0
4
[ "A002928", "A007206", "A007207" ]
[ "M4818" ]
Simon Plouffe
2024-04-27T15:06:32
oeisdata/seq/A007/A007207.seq
238315f0f0dcb1da7cf633ed23230edb
A007208
Number of letters in German name of n.
[ "4", "4", "4", "4", "4", "4", "5", "6", "4", "4", "4", "3", "5", "8", "8", "8", "8", "8", "8", "8", "7", "13", "14", "14", "14", "14", "15", "16", "14", "14", "7", "13", "14", "14", "14", "14", "15", "16", "14", "14", "7", "13", "14", "14", "14", "14", "15", "16", "14", "14", "7", "13", "14", "14", "14", "14", "15", "16", "14", "14", "7", "13", "14", "14", "14", "14", "15", "16", "14", "14", "7" ]
[ "nonn", "word" ]
57
0
1
[ "A005589", "A007005", "A007208", "A052360", "A167507" ]
[ "M3222" ]
N. J. A. Sloane.
2024-07-06T01:38:58
oeisdata/seq/A007/A007208.seq
938b8cb2654c09a197c0589dfb23db23
A007209
Number of partitions of n into parts of sizes {a( )} is a(n).
[ "1", "1", "2", "2", "4", "5", "7", "9", "12", "16", "20", "25", "32", "39", "49", "58", "73", "86", "105", "123", "149", "175", "207", "241", "284", "331", "385", "444", "515", "592", "682", "777", "894", "1015", "1160", "1310", "1492", "1683", "1903", "2140", "2412", "2708", "3037", "3395", "3801", "4239", "4730", "5254", "5852", "6489", "7204", "7965", "8823", "9741" ]
[ "nonn", "nice" ]
39
0
3
null
[ "M0315" ]
N. J. A. Sloane, Mira Bernstein
2017-05-07T22:02:36
oeisdata/seq/A007/A007209.seq
7bbfc99ba25bd9298874f034828f87bd
A007210
Oscillates under partition transform.
[ "1", "2", "3", "4", "6", "9", "11", "15", "19", "25", "31", "41", "49", "61", "75", "91", "110", "134", "157", "189", "222", "264", "308", "363", "420", "489", "566", "654", "751", "866", "985", "1130", "1283", "1462", "1655", "1877", "2115", "2387", "2684", "3018", "3379", "3791", "4225", "4724", "5257", "5855", "6500", "7219", "7990", "8850", "9777", "10802" ]
[ "nonn", "nice" ]
20
1
2
[ "A007210", "A007211" ]
[ "M0565" ]
N. J. A. Sloane, Mira Bernstein
2017-05-07T22:02:55
oeisdata/seq/A007/A007210.seq
88a175566684570dafd690b2d554d75a
A007211
Oscillates under partition transform.
[ "1", "2", "3", "5", "6", "10", "12", "17", "22", "29", "36", "48", "58", "73", "91", "111", "134", "165", "197", "236", "283", "335", "395", "468", "547", "639", "747", "866", "1001", "1160", "1334", "1530", "1757", "2007", "2286", "2606", "2958", "3349", "3793", "4281", "4821", "5430", "6097", "6833", "7657", "8559", "9549", "10652", "11858", "13178", "14639" ]
[ "nonn", "nice" ]
25
1
2
[ "A007210", "A007211", "A027593", "A130900" ]
[ "M0630" ]
N. J. A. Sloane, Mira Bernstein
2019-11-11T00:03:09
oeisdata/seq/A007/A007211.seq
bdd5379825deb43a1a335c5b236626f4
A007212
Oscillates under partition transform.
[ "1", "2", "2", "4", "4", "6", "7", "11", "12", "16", "18", "25", "28", "36", "41", "53", "59", "73", "82", "102", "115", "138", "155", "186", "209", "246", "275", "324", "363", "420", "468", "541", "605", "691", "768", "877", "976", "1103", "1222", "1380", "1530", "1716", "1895", "2122", "2343", "2609", "2872", "3192", "3514", "3890", "4269", "4716", "5172", "5697" ]
[ "nonn", "nice" ]
25
1
2
[ "A007212", "A007213", "A027595" ]
[ "M0307" ]
N. J. A. Sloane, Mira Bernstein
2019-11-11T00:03:40
oeisdata/seq/A007/A007212.seq
570b5c9c9fcab938a7fb4ab4e0d32c06
A007213
Oscillates under partition transform.
[ "1", "2", "2", "4", "4", "7", "8", "12", "13", "18", "21", "29", "33", "43", "49", "63", "71", "91", "103", "128", "143", "176", "198", "241", "271", "324", "363", "431", "483", "569", "636", "743", "827", "960", "1068", "1236", "1371", "1573", "1742", "1992", "2203", "2506", "2769", "3135", "3454", "3895", "4290", "4824", "5300", "5936", "6512", "7274", "7969" ]
[ "nonn", "nice" ]
22
1
2
[ "A007212", "A007213", "A027596" ]
[ "M0308" ]
N. J. A. Sloane, Mira Bernstein
2023-08-30T02:59:34
oeisdata/seq/A007/A007213.seq
1e55ac6b439e6faa37bd1ea71b55e67e
A007214
Low temperature antiferromagnetic susceptibility for honeycomb lattice.
[ "1", "0", "3", "2", "12", "24", "80", "222", "687", "2096", "6585", "20892", "67216", "218412", "716304", "2367696", "7881381", "26398728", "88918451", "301014786", "1023681792", "3495786472", "11983194420", "41220422022", "142247592803", "492339048156", "1708741395441", "5945617039980", "20737219258440", "72488490389592" ]
[ "nonn" ]
19
0
3
[ "A002978", "A007214" ]
[ "M2258" ]
Simon Plouffe
2021-03-03T12:13:27
oeisdata/seq/A007/A007214.seq
debbb71e36829484930c5b9621c04da3
A007215
Low temperature antiferromagnetic susceptibility for square lattice.
[ "1", "0", "4", "8", "39", "152", "672", "3016", "13989", "66664" ]
[ "nonn", "more" ]
11
0
3
null
[ "M3346" ]
Simon Plouffe
2017-11-16T15:34:49
oeisdata/seq/A007/A007215.seq
7f2f78bfda0e8ffa434f4313ba08e54f
A007216
Low temperature antiferromagnetic susceptibility for diamond.
[ "1", "0", "4", "0", "16", "24", "122", "348", "1266", "4464", "16394", "57932", "215916", "828348" ]
[ "nonn", "more" ]
13
0
3
[ "A003195", "A007216" ]
[ "M3192" ]
Simon Plouffe
2017-11-16T15:34:54
oeisdata/seq/A007/A007216.seq
8a2e2a5f0fbe3a3b21ca0ef851bd8008
A007217
Low temperature antiferromagnetic susceptibility for cubic lattice.
[ "1", "0", "0", "-2", "15", "-36", "104", "-312", "1050", "-3312", "10734", "-34518", "113210", "-370236", "1220922", "-4028696", "13364424", "-44409312" ]
[ "sign" ]
12
0
4
null
[ "M2074" ]
Simon Plouffe
2017-11-16T15:34:58
oeisdata/seq/A007/A007217.seq
ed26810ff7058562438854c2c8d1f9e0
A007218
Low temperature series for spin-1/2 Ising antiferromagnetic susceptibility for 3-dimensional b.c.c. lattice.
[ "1", "0", "0", "0", "-2", "0", "28", "-64", "39", "224", "-884", "1368", "1350", "-12272", "28752", "-11944", "-138873", "494184", "-640856", "-1111568", "7363194", "-15488224", "1198848", "93506112", "-293473869" ]
[ "sign" ]
25
0
5
[ "A003194", "A007218" ]
[ "M0039" ]
N. J. A. Sloane, Simon Plouffe
2022-02-16T10:59:17
oeisdata/seq/A007/A007218.seq
01dd9efb026fa2d93fd747885782262d
A007219
Number of golygons of order 8n (or serial isogons of order 8n).
[ "1", "28", "2108", "227322", "30276740", "4541771016", "739092675672", "127674038970623", "23085759901610016", "4327973308197103600", "835531767841066680300", "165266721954751746697155", "33364181616540879268092840" ]
[ "nonn", "easy", "nice" ]
60
1
2
[ "A006718", "A007219", "A060005", "A107350" ]
[ "M5204" ]
Simon Plouffe
2025-02-16T08:32:31
oeisdata/seq/A007/A007219.seq
98e950e441017cd168dadd7c6968484b
A007220
Almost-convex polygons of perimeter 2n on square lattice.
[ "4", "60", "588", "4636", "31932", "200364", "1174492", "6538492", "34965772", "181084796", "913687100", "4511834156", "21880671292", "104497300828", "492527133804", "2295081478492", "10588446843324", "48422608206348", "219723559153052", "990104070700956", "4433734940648588" ]
[ "nonn" ]
12
6
1
null
[ "M3692" ]
Simon Plouffe
2017-11-21T20:17:43
oeisdata/seq/A007/A007220.seq
5ca093cb3d3926a228e31c93cb962632
A007221
Almost-convex polygons of perimeter 2n on square lattice.
[ "6", "216", "3706", "44060", "417486", "3386912", "24554562", "163587572", "1020918342", "6050527496", "34395992698", "188971062108", "1009130882494", "5261414979024" ]
[ "nonn" ]
9
8
1
null
[ "M4304" ]
Simon Plouffe
2012-03-30T18:36:10
oeisdata/seq/A007/A007221.seq
a86d4e2ba35c5fba71883662a286ebb5
A007222
Almost-convex polygons of perimeter 2n on square lattice.
[ "28", "1468", "34680", "535452", "6302296", "61400920", "520788460", "3976323744", "27974148068", "184411212644", "1153389882896", "6908837566500", "39921952365008" ]
[ "nonn" ]
8
10
1
null
[ "M5203" ]
Simon Plouffe
2012-03-30T18:36:10
oeisdata/seq/A007/A007222.seq
2e7162d6034d405890bd668a7c4ddf94
A007223
Number of distinct perforation patterns for deriving (v,b) = (n+2,n) punctured convolutional codes from (2,1).
[ "1", "2", "8", "24", "85", "286", "1008", "3536", "12618", "45220", "163504", "594320", "2173197", "7983990", "29465440", "109174560", "405995326", "1514797020", "5669021488", "21275014800", "80047272578", "301892460012", "1141069157408", "4321730134624", "16399422757300" ]
[ "nonn" ]
49
2
2
[ "A000108", "A007223", "A007229", "A007595", "A274934", "A275206" ]
[ "M1843" ]
Simon Plouffe
2023-04-30T07:10:14
oeisdata/seq/A007/A007223.seq
a7249080de13e5d5159108e6644b3c77
A007224
Number of distinct perforation patterns for deriving (v,b) = (n+3,n) punctured convolutional codes from (2,1).
[ "2", "9", "38", "143", "546", "2066", "7752", "29070", "108968", "408595", "1533870", "5766243", "21710850", "81880920", "309328008", "1170524970", "4436618940", "16842720336", "64037794548", "243836217702", "929759970392", "3549992610584", "13571935767600", "51950354135888" ]
[ "nonn" ]
30
4
1
[ "A007223", "A007224", "A007229" ]
[ "M1933" ]
Simon Plouffe
2023-03-09T08:28:56
oeisdata/seq/A007/A007224.seq
ade541eeca4d324ceb19a8c5e48f0e12
A007225
Number of distinct perforation patterns for deriving (v,b) = (n+4,n) punctured convolutional codes from (2,1).
[ "2", "12", "52", "232", "952", "3888", "15504", "61333", "240350", "937508", "3641820", "14112560", "54587280", "210907168", "814278240", "3142611402", "12126758436", "46796872472", "180619420520", "697320058864", "2693097842512", "10405151052320", "40219629005920" ]
[ "nonn" ]
28
5
1
[ "A007223", "A007224", "A007225", "A007229" ]
[ "M2023" ]
Simon Plouffe
2023-03-10T03:18:47
oeisdata/seq/A007/A007225.seq
a2d008372e56f7fdc0a5bdba9947118f
A007226
a(n) = 2*det(M(n; -1))/det(M(n; 0)), where M(n; m) is the n X n matrix with (i,j)-th element equal to 1/binomial(n + i + j + m, n).
[ "2", "3", "10", "42", "198", "1001", "5304", "29070", "163438", "937365", "5462730", "32256120", "192565800", "1160346492", "7048030544", "43108428198", "265276342782", "1641229898525", "10202773534590", "63698396932170", "399223286267190", "2510857763851185", "15842014607109600" ]
[ "nonn", "easy" ]
153
0
1
[ "A000139", "A006013", "A007223", "A007224", "A007225", "A007226", "A007227", "A007228", "A007229", "A124724" ]
[ "M4701" ]
Simon Plouffe
2025-03-25T08:45:45
oeisdata/seq/A007/A007226.seq
dc628066accbd9e9e81362663252e7b7
A007227
Number of distinct perforation patterns for deriving (v,b) = (n+2,n) punctured convolutional codes from (3,1).
[ "9", "42", "236", "1287", "7314", "41990", "245256", "1448655", "8649823", "52106040", "316360752", "1933910820", "11893566078", "73537906926", "456864894288", "2850557192175", "17854854154215", "112230508880490", "707714010205020", "4475876883386895" ]
[ "nonn" ]
28
2
1
[ "A007223", "A007224", "A007225", "A007227", "A007229" ]
[ "M4624" ]
Simon Plouffe
2020-07-28T02:47:22
oeisdata/seq/A007/A007227.seq
303475c371707850ec389c0eff14b9a3
A007228
a(n) = 3*binomial(4*n,n)/(n+1).
[ "3", "6", "28", "165", "1092", "7752", "57684", "444015", "3506100", "28242984", "231180144", "1917334783", "16077354108", "136074334200", "1160946392760", "9973891723635", "86210635955220", "749191930237608", "6541908910355280", "57369142749576660", "505045163173167760", "4461713825057817120" ]
[ "nonn", "easy" ]
92
0
1
[ "A002293", "A006632", "A007223", "A007224", "A007225", "A007226", "A007227", "A007228", "A007229", "A124724", "A263133" ]
[ "M5200" ]
Simon Plouffe
2024-01-05T23:32:28
oeisdata/seq/A007/A007228.seq
be86807a3b046e059a32d4f1792835fb
A007229
Number of distinct perforation patterns for deriving (v,b) = (n+2,n) punctured convolutional codes from (4,1).
[ "38", "264", "2016", "15504", "122661", "986700", "8064576", "66756144", "558689224", "4719593312", "40193414112", "344721646640", "2974925353455", "25814778578820", "225105551191680", "1971557711151600", "17336058626562984", "152984380665537760" ]
[ "nonn" ]
47
2
1
null
[ "M5267" ]
Simon Plouffe
2023-02-17T07:38:38
oeisdata/seq/A007/A007229.seq
ddcfee154edab0c616f21dec00fcbb8e
A007230
Number of free subsets of multiplicative group of GF(2^n).
[ "0", "1", "2", "7", "12", "30", "54", "127", "226", "508", "930", "2046", "3780", "8182", "15288", "32767", "61680", "131042", "248346", "524284" ]
[ "nonn" ]
13
1
3
null
[ "M1738" ]
Simon Plouffe
2015-01-30T21:56:28
oeisdata/seq/A007/A007230.seq
a34c9ccf96ccf5ae616137ec98a962db
A007231
Number of free subsets of multiplicative group of GF(3^n).
[ "1", "5", "13", "52", "121", "455", "1093", "4305", "9841", "36905", "88573", "348728", "797161", "2989355", "7174453", "28585712", "64570081", "242137805", "581130733", "2288202262" ]
[ "nonn" ]
12
1
2
null
[ "M3835" ]
Simon Plouffe
2015-01-30T21:56:45
oeisdata/seq/A007/A007231.seq
78c7762ea8c155c0ebcf8ff5c46654e3
A007232
Number of free subsets of multiplicative group of GF(5^n).
[ "2", "15", "74", "409", "1951", "9765", "48827", "256347", "1220699", "6103515", "30517572", "160216158", "762939452", "3814697265", "19073486293", "101327896117", "476837158134" ]
[ "nonn" ]
15
1
1
[ "A007232", "A007233" ]
[ "M2077" ]
Simon Plouffe
2018-03-22T09:48:00
oeisdata/seq/A007/A007232.seq
910be4e0d222696f7bd31a1eef7d0897
A007233
Number of free subsets of multiplicative group of GF(7^n).
[ "3", "31", "171", "1575", "8403", "77206", "411771", "3828187", "20176803", "185374380", "988663371", "9083344725", "48444505203", "445083891551", "2373780754971", "22068742956375" ]
[ "nonn" ]
17
1
1
[ "A007232", "A007233" ]
[ "M3127" ]
Simon Plouffe
2018-03-22T09:48:13
oeisdata/seq/A007/A007233.seq
870e2edeedec5994bf9bacc2ad8fb6c0
A007234
Number of (x -> x^2)-free subsets of symmetric group.
[ "0", "1", "4", "16", "72", "522", "3642", "30753" ]
[ "nonn", "more" ]
14
1
3
null
[ "M3523" ]
Simon Plouffe
2015-01-31T09:55:18
oeisdata/seq/A007/A007234.seq
83d73a0b62c54f5014e7b115e15edb81
A007235
Structure constants for certain representations of S_n.
[ "8", "27", "384", "12100", "736128", "70990416", "9939419136", "1896254551296", "472882821120000", "149328979405056000", "58255835226557644800", "27519543889780053196800", "15483244831426302168268800", "10231838708930053383168000000" ]
[ "nonn" ]
15
1
1
null
[ "M4500" ]
Simon Plouffe
2024-05-22T11:33:05
oeisdata/seq/A007/A007235.seq
7a99b1da8869da8f84d7d33e78aff7d7
A007236
Compressibility of hard-hexagon lattice gas model.
[ "1", "-7", "18", "-24", "24", "6", "66", "258", "1014", "3906", "14760", "54696", "198510", "704010", "2431110", "8130096", "26103624", "79292226", "221534442", "532863372", "870102906", "-842584128", "-17420140980", "-111985825752", "-559952980782", "-2460921694668", "-9861404819574", "-36339628229910" ]
[ "sign" ]
13
0
2
null
[ "M4357" ]
Simon Plouffe
2019-11-19T05:57:08
oeisdata/seq/A007/A007236.seq
f39362a3071ad3fdcaf556a47dad4e46
A007237
Number of triangles with integer sides and area = n times perimeter.
[ "5", "18", "45", "45", "52", "139", "80", "89", "184", "145", "103", "312", "96", "225", "379", "169", "116", "498", "123", "328", "560", "280", "134", "592", "228", "271", "452", "510", "134", "1036", "144", "280", "639", "339", "597", "1119", "139", "354", "635", "648", "162", "1486", "169", "594", "1215", "354", "186", "1066", "369", "622", "706", "597", "164" ]
[ "nonn" ]
48
1
1
[ "A007237", "A120062" ]
[ "M3878" ]
Simon Plouffe
2023-12-27T09:02:31
oeisdata/seq/A007/A007237.seq
0c16e2e1c3a702c51fd776c0fbb75c14
A007238
Length of longest chain of subgroups in S_n.
[ "0", "1", "2", "4", "5", "6", "7", "10", "11", "12", "13", "15", "16", "17", "18", "22", "23", "24", "25", "27", "28", "29", "30", "33", "34", "35", "36", "38", "39", "40", "41", "46", "47", "48", "49", "51", "52", "53", "54", "57", "58", "59", "60", "62", "63", "64", "65", "69", "70", "71", "72", "74", "75", "76", "77", "80", "81", "82", "83", "85", "86", "87", "88", "94", "95", "96", "97", "99", "100", "101" ]
[ "nonn", "nice" ]
45
1
3
null
[ "M0945" ]
N. J. A. Sloane, Simon Plouffe
2021-11-20T14:16:21
oeisdata/seq/A007/A007238.seq
ec990ce83d83dc2c0dc72fb8ffd137d1
A007239
Energy function for hexagonal lattice.
[ "3", "6", "12", "24", "54", "138", "378", "1080", "3186", "9642", "29784", "93552", "297966", "960294", "3126408", "10268688", "33989388", "113277582", "379833906", "1280618784", "4339003044", "14767407522", "50464951224", "173099580168", "595786322292", "2057106617226", "7123467773790", "24734460619704" ]
[ "nonn" ]
18
1
1
[ "A002908", "A007239" ]
[ "M2562" ]
Simon Plouffe
2022-02-14T07:31:39
oeisdata/seq/A007/A007239.seq
718f2d31249f4a9977a5662705c6c55e
A007240
McKay-Thompson series of class 1A for the Monster group with a(0) = 24.
[ "1", "24", "196884", "21493760", "864299970", "20245856256", "333202640600", "4252023300096", "44656994071935", "401490886656000", "3176440229784420", "22567393309593600", "146211911499519294", "874313719685775360", "4872010111798142520", "25497827389410525184" ]
[ "nonn", "easy", "nice" ]
70
-1
2
[ "A000521", "A007240", "A008408", "A014708" ]
[ "M5179" ]
N. J. A. Sloane
2021-03-12T22:24:41
oeisdata/seq/A007/A007240.seq
ceb922541aa9e1758a7528dab8b96373
A007241
McKay-Thompson series of class 2A for the Monster group with a(0) = 24.
[ "1", "24", "4372", "96256", "1240002", "10698752", "74428120", "431529984", "2206741887", "10117578752", "42616961892", "166564106240", "611800208702", "2125795885056", "7040425608760", "22327393665024", "68134255043715", "200740384538624" ]
[ "nonn", "nice" ]
54
-1
2
[ "A007241", "A007267", "A045478", "A101558", "A106207" ]
[ "M5176" ]
N. J. A. Sloane
2021-12-17T11:05:43
oeisdata/seq/A007/A007241.seq
6f8fe4b73bed5d5b632c3a2b9b11af56
A007242
McKay-Thompson series of class 2a for the Monster group.
[ "1", "-492", "-22590", "-367400", "-3764865", "-28951452", "-182474434", "-990473160", "-4780921725", "-20974230680", "-84963769662", "-321583404672", "-1147744866180", "-3890805976500", "-12601590210180", "-39183052547592", "-117437602167291", "-340431109329600", "-957251463332600", "-2617490612355240", "-6975126788952456", "-18149106017123576", "-46187557595906250" ]
[ "sign" ]
90
0
2
[ "A000521", "A007242", "A014708", "A106203", "A289061", "A289063", "A289330", "A289331", "A289332", "A289333", "A289334" ]
[ "M5455" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007242.seq
124eba5ec42235257ee776889f883947
A007243
McKay-Thompson series of class 3A for the Monster group with a(0) = 0.
[ "1", "0", "783", "8672", "65367", "371520", "1741655", "7161696", "26567946", "90521472", "288078201", "864924480", "2469235686", "6748494912", "17746495281", "45086909440", "111066966315", "266057139456", "621284327856", "1417338712800", "3164665156308" ]
[ "nonn", "nice", "easy" ]
37
-1
3
[ "A007243", "A030197", "A045480" ]
[ "M5480" ]
N. J. A. Sloane
2017-04-01T05:42:05
oeisdata/seq/A007/A007243.seq
1c10304b3b520e07c77119cf985d4cd0
A007244
McKay-Thompson series of class 3B for the Monster group.
[ "1", "0", "54", "-76", "-243", "1188", "-1384", "-2916", "11934", "-11580", "-21870", "79704", "-71022", "-123444", "421308", "-352544", "-581013", "1885572", "-1510236", "-2388204", "7469928", "-5777672", "-8852004", "26869968", "-20218587", "-30177684", "89408826" ]
[ "sign", "easy", "nice" ]
29
-1
3
[ "A007244", "A030182", "A045481" ]
[ "M5310" ]
N. J. A. Sloane
2017-10-09T21:48:38
oeisdata/seq/A007/A007244.seq
61064a55e5f42755c597769d97291e7b
A007245
McKay-Thompson series of class 3C for the Monster group.
[ "1", "248", "4124", "34752", "213126", "1057504", "4530744", "17333248", "60655377", "197230000", "603096260", "1749556736", "4848776870", "12908659008", "33161242504", "82505707520", "199429765972", "469556091240", "1079330385764", "2426800117504", "5346409013164" ]
[ "nonn", "easy", "nice" ]
80
0
2
[ "A000521", "A007245" ]
[ "M5423" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007245.seq
b38ca8aac9f8528fb65ab8556dacaf8f
A007246
McKay-Thompson series of class 2B for the Monster group.
[ "1", "0", "276", "-2048", "11202", "-49152", "184024", "-614400", "1881471", "-5373952", "14478180", "-37122048", "91231550", "-216072192", "495248952", "-1102430208", "2390434947", "-5061476352", "10487167336", "-21301241856", "42481784514", "-83300614144" ]
[ "sign", "easy", "nice" ]
47
-1
3
[ "A007191", "A007246", "A035099", "A045479", "A097340", "A107080", "A134786" ]
[ "M5434" ]
N. J. A. Sloane
2021-03-12T22:24:41
oeisdata/seq/A007/A007246.seq
d2153fc2352cfca03177116cb8595a1c
A007247
McKay-Thompson series of class 4B for the Monster group.
[ "1", "52", "834", "4760", "24703", "94980", "343998", "1077496", "3222915", "8844712", "23381058", "58359168", "141244796", "327974700", "742169724", "1627202744", "3490345477", "7301071680", "14987511560", "30138820888", "59623576440", "115928963656" ]
[ "nonn" ]
47
0
2
[ "A007247", "A007249", "A022577" ]
[ "M5305" ]
N. J. A. Sloane
2025-02-28T09:37:52
oeisdata/seq/A007/A007247.seq
e2909f3ecc7e7e3386b17ee73db0a2c4
A007248
McKay-Thompson series of class 4C for the Monster group.
[ "1", "20", "-62", "216", "-641", "1636", "-3778", "8248", "-17277", "34664", "-66878", "125312", "-229252", "409676", "-716420", "1230328", "-2079227", "3460416", "-5677816", "9198424", "-14729608", "23328520", "-36567242", "56774712", "-87369461", "133321908", "-201825396", "303248408", "-452431503" ]
[ "sign", "easy" ]
34
0
2
[ "A000521", "A007240", "A007241", "A007248", "A007267", "A014708", "A029845", "A045478", "A097243", "A124972" ]
[ "M5084" ]
N. J. A. Sloane
2017-01-01T11:24:04
oeisdata/seq/A007/A007248.seq
b6ffa1b5ef07c16a36351e5817fa7a35
A007249
McKay-Thompson series of class 4D for the Monster group.
[ "1", "-12", "66", "-232", "639", "-1596", "3774", "-8328", "17283", "-34520", "66882", "-125568", "229244", "-409236", "716412", "-1231048", "2079237", "-3459264", "5677832", "-9200232", "14729592", "-23325752", "36567222", "-56778888", "87369483", "-133315692" ]
[ "sign" ]
50
0
2
[ "A007191", "A007249", "A022577", "A112142", "A286352" ]
[ "M4846" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007249.seq
00f037888574e499b81d8e1f1fd75b66
A007250
McKay-Thompson series of class 4a for the Monster group.
[ "1", "-76", "-702", "-5224", "-23425", "-98172", "-336450", "-1094152", "-3188349", "-8913752", "-23247294", "-58610304", "-140786308", "-328793172", "-740736900", "-1629664840", "-3486187003", "-7307990208", "-14976155896", "-30157221352", "-59594117256", "-115975615160", "-222119374922", "-419704427016" ]
[ "sign", "easy" ]
67
0
2
[ "A007242", "A007249", "A007250", "A007260", "A022577" ]
[ "M5353" ]
N. J. A. Sloane
2021-02-14T01:16:32
oeisdata/seq/A007/A007250.seq
c0cf94276940c73ed59bf5abfcaef119
A007251
McKay-Thompson series of class 5A for the Monster group.
[ "1", "0", "134", "760", "3345", "12256", "39350", "114096", "307060", "776000", "1867170", "4298600", "9540169", "20487360", "42756520", "86967184", "172859325", "336450560", "642489660", "1205572920", "2226005750", "4049168800", "7264172196", "12864273920" ]
[ "nonn" ]
29
-1
3
[ "A007251", "A045482", "A244745" ]
[ "M5396" ]
N. J. A. Sloane.
2017-04-01T04:47:47
oeisdata/seq/A007/A007251.seq
6cfc034057a5d2baf3757cd76f0e876a
A007252
McKay-Thompson series of class 5B for the Monster group with a(0) = 0.
[ "1", "0", "9", "10", "-30", "6", "-25", "96", "60", "-250", "45", "-150", "544", "360", "-1230", "184", "-675", "2310", "1410", "-4830", "750", "-2450", "8196", "4920", "-16180", "2376", "-7875", "25644", "15000", "-48720", "7126", "-22800", "73221", "42310", "-134760", "19284", "-61400", "194334", "110610", "-349000", "49563", "-155250", "486370" ]
[ "sign" ]
32
-1
3
[ "A007252", "A045483", "A106248" ]
[ "M4599" ]
N. J. A. Sloane
2017-01-01T09:56:20
oeisdata/seq/A007/A007252.seq
69a7e430999ec3bc3df3a59e3b8b217c
A007253
McKay-Thompson series of class 5a for Monster.
[ "1", "0", "-6", "20", "15", "36", "0", "-84", "195", "100", "240", "0", "-461", "1020", "540", "1144", "0", "-1980", "4170", "2040", "4275", "0", "-6984", "14340", "6940", "14076", "0", "-21936", "44025", "20760", "41476", "0", "-62484", "123620", "57630", "113244", "0", "-166056", "324120", "148900", "289578", "0" ]
[ "sign" ]
47
-1
3
[ "A000521", "A007253" ]
[ "M4131" ]
N. J. A. Sloane
2024-12-10T13:13:55
oeisdata/seq/A007/A007253.seq
46d8ae579aba27979b0ffbcd6cdaac25
A007254
McKay-Thompson series of class 6A for Monster.
[ "1", "0", "79", "352", "1431", "4160", "13015", "31968", "81162", "183680", "412857", "864320", "1805030", "3564864", "7000753", "13243392", "24805035", "45168896", "81544240", "143832672", "251550676", "432030080", "735553575", "1233715328", "2052941733" ]
[ "nonn" ]
31
-1
3
[ "A007254", "A045484" ]
[ "M5355" ]
N. J. A. Sloane
2018-05-11T01:51:15
oeisdata/seq/A007/A007254.seq
7603b77a97498d59fec85bac4284502d
A007255
McKay-Thompson series of class 6B for Monster.
[ "1", "0", "78", "364", "1365", "4380", "12520", "32772", "80094", "185276", "409578", "871272", "1792754", "3582708", "6977100", "13277472", "24747867", "45267324", "81389908", "144048396", "251265288", "432425864", "734953116", "1234647216", "2051576037" ]
[ "nonn" ]
27
-1
3
[ "A007255", "A045485", "A121665" ]
[ "M5354" ]
N. J. A. Sloane
2018-06-26T08:40:19
oeisdata/seq/A007/A007255.seq
ea9e5c18f41876aa0736d288a0a7405e
A007256
McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
[ "1", "0", "15", "-32", "87", "-192", "343", "-672", "1290", "-2176", "3705", "-6336", "10214", "-16320", "25905", "-39936", "61227", "-92928", "138160", "-204576", "300756", "-435328", "626727", "-897408", "1271205", "-1790592", "2508783", "-3487424", "4824825", "-6641664", "9083400", "-12371904", "16778784", "-22630912", "30407112", "-40703040", "54238342", "-72018624" ]
[ "sign" ]
25
-1
3
[ "A007256", "A045486" ]
[ "M4962" ]
N. J. A. Sloane
2017-10-09T21:48:45
oeisdata/seq/A007/A007256.seq
4058043f4000e31988a790da6ce06fc3
A007257
McKay-Thompson series of class 6D for Monster.
[ "1", "0", "-2", "28", "-27", "-52", "136", "-108", "-162", "620", "-486", "-760", "1970", "-1404", "-1940", "6048", "-4293", "-6100", "15796", "-10692", "-14264", "40232", "-27108", "-36496", "93285", "-61020", "-79054", "211624", "-137781", "-179296", "451680", "-288360", "-365780" ]
[ "sign" ]
22
-1
3
[ "A007257", "A045487" ]
[ "M2147" ]
N. J. A. Sloane
2018-06-02T21:27:24
oeisdata/seq/A007/A007257.seq
bff8ea91ae740c7b2bb1196dc5fa3963
A007258
McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).
[ "1", "0", "6", "4", "-3", "-12", "-8", "12", "30", "20", "-30", "-72", "-46", "60", "156", "96", "-117", "-300", "-188", "228", "552", "344", "-420", "-1008", "-603", "732", "1770", "1048", "-1245", "-2976", "-1776", "2088", "4908", "2900", "-3420", "-7992", "-4658", "5460", "12756", "7408", "-8583", "-19944", "-11564", "13344", "30756", "17744", "-20448", "-46944", "-26916" ]
[ "sign" ]
27
-1
3
[ "A007258", "A045488" ]
[ "M4052" ]
N. J. A. Sloane
2018-05-09T22:58:22
oeisdata/seq/A007/A007258.seq
eee07fd42f31673dd9758f7079be10b5
A007259
Expansion of Product_{m>=1} (1 + q^m)^(-8).
[ "1", "-8", "28", "-64", "134", "-288", "568", "-1024", "1809", "-3152", "5316", "-8704", "13990", "-22208", "34696", "-53248", "80724", "-121240", "180068", "-264448", "384940", "-556064", "796760", "-1132544", "1598789", "-2243056", "3127360", "-4333568", "5971922", "-8188096", "11170160", "-15163392", "20491033", "-27572936" ]
[ "sign", "easy", "nice" ]
51
0
2
[ "A007259", "A007263", "A014705", "A022573", "A286352" ]
[ "M4504" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007259.seq
9113691822cd72eac56ca39dc8a818cf
A007260
McKay-Thompson series of class 6a for Monster.
[ "1", "-33", "-153", "-713", "-2550", "-7479", "-20314", "-51951", "-122229", "-276656", "-601068", "-1254105", "-2541531", "-5018721", "-9647991", "-18168984", "-33554784", "-60818040", "-108471674", "-190607871", "-330140403", "-564580142", "-953980392", "-1593599832", "-2634301308", "-4311874755", "-6991318008" ]
[ "sign" ]
40
0
2
[ "A007242", "A007250", "A007260", "A007262", "A121596", "A258917" ]
[ "M5238" ]
N. J. A. Sloane.
2021-02-14T01:17:26
oeisdata/seq/A007/A007260.seq
7b53309ebbd43211505dd31c6c63f04d
A007261
McKay-Thompson series of class 6b for the Monster group.
[ "1", "21", "171", "745", "2418", "7587", "20510", "51351", "122715", "277384", "598812", "1255761", "2543973", "5011725", "9653013", "18176040", "33535032", "60831648", "108490390", "190557015", "330174837", "564626278", "953857104", "1593681480", "2634409140", "4311592119", "6991502688", "11237020682", "17909802270" ]
[ "nonn" ]
57
0
2
[ "A007261", "A030197", "A058537" ]
[ "M5111" ]
N. J. A. Sloane
2017-11-27T03:24:54
oeisdata/seq/A007/A007261.seq
db8044660300e474ddd5d08ea16c0c83
A007262
McKay-Thompson series of class 6c for Monster.
[ "1", "-6", "9", "16", "-66", "54", "98", "-300", "243", "364", "-1128", "828", "1221", "-3498", "2511", "3528", "-9876", "6804", "9358", "-25428", "17217", "23068", "-61644", "40824", "53916", "-141318", "92340", "119912", "-310554", "199980", "256792", "-656436", "418311", "530960", "-1344144", "847584", "1066157", "-2673372", "1671741", "2084464", "-5186118", "3216834", "3981926", "-9832752", "6057504", "7445924", "-18269124", "11181636", "13661725", "-33315852", "20274948", "24630344", "-59740716" ]
[ "sign" ]
43
0
2
[ "A007262", "A132107" ]
[ "M4078" ]
N. J. A. Sloane
2021-08-22T13:43:19
oeisdata/seq/A007/A007262.seq
d696c9046d151824b1e739e0efcbf176
A007263
Coefficients of completely replicable function "6d".
[ "1", "0", "16", "-8", "0", "128", "28", "0", "576", "-64", "0", "2048", "134", "0", "6304", "-288", "0", "17408", "568", "0", "44416", "-1024", "0", "106496", "1809", "0", "242480", "-3152", "0", "528896", "5316", "0", "1112128", "-8704", "0", "2265088", "13990", "0", "4486112" ]
[ "sign" ]
41
-1
3
[ "A007259", "A007263", "A022573" ]
[ "M4995" ]
N. J. A. Sloane
2019-11-20T11:37:11
oeisdata/seq/A007/A007263.seq
0427e3d6ba9b00fa602e81766c51e2a2
A007264
McKay-Thompson series of class 7A for Monster.
[ "1", "0", "51", "204", "681", "1956", "5135", "12360", "28119", "60572", "125682", "251040", "487426", "920568", "1699611", "3070508", "5445510", "9490116", "16283793", "27537708", "45959775", "75760640", "123471327", "199081632", "317814988" ]
[ "nonn" ]
28
-1
3
[ "A007264", "A030183", "A045489" ]
[ "M5302" ]
N. J. A. Sloane
2018-05-11T01:50:54
oeisdata/seq/A007/A007264.seq
b14403ef318928aeee298d931dbda543
A007265
McKay-Thompson series of class 8A for Monster.
[ "1", "0", "36", "128", "386", "1024", "2488", "5632", "12031", "24576", "48308", "91904", "170110", "307200", "542872", "941056", "1602819", "2686976", "4439688", "7238272", "11657090", "18561024", "29242240", "45617664", "70507772" ]
[ "nonn" ]
21
-1
3
[ "A007265", "A045490" ]
[ "M5252" ]
N. J. A. Sloane
2017-10-09T19:10:17
oeisdata/seq/A007/A007265.seq
477e5c7e1d30e28ba4f1eb7e79cd784c
A007266
McKay-Thompson series of class 9A for Monster.
[ "1", "0", "27", "86", "243", "594", "1370", "2916", "5967", "11586", "21870", "39852", "71052", "123444", "210654", "352480", "581013", "942786", "1510254", "2388204", "3734964", "5777788", "8852004", "13434984", "20218395", "30177684", "44704413", "65743348", "96033357", "139368816" ]
[ "nonn" ]
32
-1
3
[ "A007266", "A045491" ]
[ "M5192" ]
N. J. A. Sloane, Apr 28 1994
2017-05-02T12:37:52
oeisdata/seq/A007/A007266.seq
8403a7c2f9130ed01255f47d0efa36fa
A007267
Expansion of 16 * (1 + k^2)^4 /(k * k'^2)^2 in powers of q where k is the Jacobian elliptic modulus, k' the complementary modulus and q is the nome.
[ "1", "104", "4372", "96256", "1240002", "10698752", "74428120", "431529984", "2206741887", "10117578752", "42616961892", "166564106240", "611800208702", "2125795885056", "7040425608760", "22327393665024", "68134255043715", "200740384538624" ]
[ "nonn", "nice" ]
54
-1
2
[ "A007241", "A007247", "A007267", "A045478", "A101558", "A106207" ]
[ "M5369" ]
N. J. A. Sloane, Apr 28 1994
2021-03-12T22:24:41
oeisdata/seq/A007/A007267.seq
c2ba6905656977624e730459de361161
A007268
Number of partition graphs on n vertices.
[ "1", "0", "1", "2", "5", "14", "47", "186", "894", "5249", "38181", "348568" ]
[ "nonn", "more", "hard" ]
15
1
4
null
[ "M1467" ]
Simon Plouffe
2017-12-05T10:13:57
oeisdata/seq/A007/A007268.seq
6673689d3f8f14185137eac362d48107
A007269
General partition graphs on n vertices.
[ "1", "1", "2", "5", "13", "41", "145", "604", "2938", "16947", "117208", "988832" ]
[ "nonn", "more", "hard" ]
13
1
3
null
[ "M1451" ]
Simon Plouffe
2017-12-03T13:35:03
oeisdata/seq/A007/A007269.seq
9f2c2e9fa133c03c1f78836d908aa5a2
A007270
Low-temperature series for magnetization in zero-field 3-state Potts model on cubic lattice.
[ "1", "0", "0", "0", "0", "0", "-3", "0", "0", "0", "-18", "-18", "42", "0", "-135", "-270", "477", "648", "-1980", "-2988", "4140", "14052", "-21690", "-52920", "55020", "201852", "-162774", "-914538", "555750", "3229524", "-1188327", "-13301370", "1402686", "52334268", "95751", "-195398208", "-58983558", "761838084", "359664885", "-2910516786", "-1946958399", "10681132140", "10207745148", "-40522674258" ]
[ "sign" ]
24
0
7
[ "A002929", "A007270", "A007271", "A057374", "A057382", "A057390", "A057398" ]
[ "M2194" ]
Simon Plouffe
2024-11-19T01:04:23
oeisdata/seq/A007/A007270.seq
f7fcd74fca477d15b072cb76c6acf5ff
A007271
Zero-field low-temperature series for 3-state Potts model.
[ "1", "0", "0", "0", "0", "0", "0", "0", "-3", "0", "0", "0", "0", "0", "-24", "-24", "54", "0", "0", "0", "-252", "-504", "900", "1152", "-1452", "-3312", "-7344", "11484", "35856", "-30132", "-50184", "264", "-113160", "175464", "712176", "-319098", "-1997856", "334320", "341856", "1211472", "13301112", "-2785392" ]
[ "sign" ]
8
0
9
null
[ "M2192" ]
Simon Plouffe
2012-03-30T18:36:11
oeisdata/seq/A007/A007271.seq
00b47178ab05e3a45b1c53a5a23c29ce
A007272
Super ballot numbers: 60(2n)!/(n!(n+3)!).
[ "10", "5", "6", "10", "20", "45", "110", "286", "780", "2210", "6460", "19380", "59432", "185725", "589950", "1900950", "6203100", "20470230", "68234100", "229514700", "778354200", "2659376850", "9148256364", "31667041260", "110248217720", "385868762020", "1357193576760", "4795417304552", "17015996887120", "60619488910365" ]
[ "nonn", "easy" ]
59
0
1
[ "A001622", "A002422", "A007054", "A007272", "A135573", "A348893" ]
[ "M4676" ]
N. J. A. Sloane, Simon Plouffe, Ira M. Gessel
2025-01-20T10:51:16
oeisdata/seq/A007/A007272.seq
4ea9d932122f2abf0103acf2cdbaccbc
A007273
Inverse of 1155th cyclotomic polynomial.
[ "1", "1", "1", "0", "0", "-1", "-1", "-2", "-1", "-1", "0", "-1", "0", "0", "1", "1", "2", "2", "2", "1", "0", "0", "-1", "-1", "-2", "-1", "-2", "-1", "-2", "0", "0", "2", "1", "3", "2", "3", "1", "1", "-1", "-1", "-3", "-3", "-3", "-2", "-2", "-1", "0", "1", "2", "2", "3", "3", "3", "1", "1", "0", "0", "-2", "-2", "-3", "-2", "-3", "-2", "-1", "1", "1", "2", "2", "3", "2", "2", "1", "1", "-1", "-2", "-3", "-2", "-2", "-1", "-1", "0" ]
[ "sign" ]
24
0
8
null
[ "M0047" ]
Simon Plouffe
2017-04-07T11:33:14
oeisdata/seq/A007/A007273.seq
bf575c7c83ea884a8cc81f77eda5a914
A007274
Walks on hexagonal lattice using each point at most twice.
[ "1", "6", "36", "216", "1260", "7206", "40650", "227256", "1262832", "6983730", "38470224", "211220814", "1156489782", "6317095284", "34435495872", "187380150468", "1018035642054" ]
[ "nonn", "walk" ]
14
0
2
[ "A001334", "A007274", "A007275" ]
[ "M4222" ]
Simon Plouffe
2022-02-02T16:06:29
oeisdata/seq/A007/A007274.seq
a875a02561d8ea008fab8b5ab6030cfd
A007275
Walks on hexagonal lattice using each point at most three times.
[ "1", "6", "36", "216", "1296", "7776", "46440", "276054", "1633848", "9633366", "56616132", "331847118", "1940715960", "11327957196", "66010769382", "384094025382", "2231978658906" ]
[ "nonn", "walk" ]
15
0
2
[ "A001334", "A007274", "A007275" ]
[ "M4223" ]
Simon Plouffe
2017-12-05T10:14:05
oeisdata/seq/A007/A007275.seq
a5210abc602c7447a57f7572a510784e
A007276
Expansion of free energy series related to Potts model.
[ "18", "72", "336", "1728", "9981", "57624", "359412", "2271552" ]
[ "nonn" ]
7
4
1
null
[ "M5056" ]
Simon Plouffe
2012-03-30T18:36:11
oeisdata/seq/A007/A007276.seq
c95db6f6d2d14524b7495591b2461e5f
A007277
Expansion of susceptibility series related to Potts model.
[ "3", "18", "105", "636", "3807", "23094", "140469", "857736", "5251163", "32230218" ]
[ "nonn" ]
7
1
1
null
[ "M3047" ]
Simon Plouffe
2012-03-30T18:36:11
oeisdata/seq/A007/A007277.seq
2f3102bcb389427c35482d15f4e6d08d
A007278
Expansion of susceptibility series related to Potts model.
[ "4", "32", "252", "2032", "16292", "132000", "1070716", "8729216", "71320324", "584550656" ]
[ "nonn", "more" ]
11
1
1
null
[ "M3644" ]
Simon Plouffe
2022-02-09T18:05:48
oeisdata/seq/A007/A007278.seq
d076940d53e91d04fc4897e3973b1b04
A007279
Number of partitions of n into partition numbers.
[ "1", "1", "2", "3", "4", "6", "8", "11", "14", "18", "23", "29", "36", "44", "54", "66", "79", "95", "113", "133", "157", "184", "216", "250", "290", "335", "385", "442", "505", "576", "656", "743", "842", "951", "1070", "1204", "1351", "1514", "1691", "1887", "2102", "2336", "2595", "2875", "3184", "3519", "3883", "4282", "4713", "5181", "5690", "6241", "6839", "7482" ]
[ "nonn" ]
53
0
3
[ "A000041", "A007279", "A086209", "A229362" ]
[ "M0558" ]
N. J. A. Sloane, Mira Bernstein
2018-06-23T03:11:21
oeisdata/seq/A007/A007279.seq
339a38576730baef220aca03819c3d13
A007280
Multiplicative encoding of partition triangle.
[ "2", "6", "30", "630", "34650", "47297250", "309560501250", "618190773193743750", "66537433850544954015468750", "65572844234095125006030612749369531250", "70740128442809835497514843888197127919441136894531250" ]
[ "nonn" ]
14
1
1
[ "A000040", "A007280" ]
[ "M1694" ]
N. J. A. Sloane.
2017-12-03T18:27:48
oeisdata/seq/A007/A007280.seq
0bd80670a016eae7ec2cf9164ec28dc0
A007281
Number of `(n,2)'-sequences of length 2n.
[ "1", "1", "2", "2", "5", "4", "8", "6", "1", "0", "1", "0", "0" ]
[ "nonn", "hard", "more" ]
18
1
3
null
[ "M0605" ]
Hong-Yeop Song (hysong(AT)yonsei.ac.kr)
2020-03-03T10:27:06
oeisdata/seq/A007/A007281.seq
25aecc1f75833ad1eb6591e22e92b895
A007282
Number of hexaflexagons with 3n triangles that can be folded from a straight strip of paper.
[ "1", "1", "1", "4", "14", "74", "434", "2876", "19848", "143306", "1062149", "8058223", "62259820", "488630360", "3886211100", "31267852668" ]
[ "nonn", "more", "nice" ]
15
1
4
[ "A000207", "A001683", "A007282" ]
[ "M3489" ]
N. J. A. Sloane, frb6006(AT)cs.rit.edu (Frank R. Bernhart)
2022-11-19T01:10:34
oeisdata/seq/A007/A007282.seq
aba4cf0256b8b257f2aede707f8b7f8e
A007283
a(n) = 3*2^n.
[ "3", "6", "12", "24", "48", "96", "192", "384", "768", "1536", "3072", "6144", "12288", "24576", "49152", "98304", "196608", "393216", "786432", "1572864", "3145728", "6291456", "12582912", "25165824", "50331648", "100663296", "201326592", "402653184", "805306368", "1610612736", "3221225472", "6442450944", "12884901888" ]
[ "easy", "nonn" ]
254
0
1
[ "A000079", "A000315", "A001630", "A002860", "A003090", "A003191", "A003945", "A007283", "A029744", "A029747", "A029748", "A029750", "A029858", "A040082", "A042950", "A054886", "A067771", "A078042", "A093562", "A096231", "A096940", "A098679", "A098843", "A098846", "A099321", "A100540", "A124508", "A133466", "A163511", "A163876", "A179070", "A193277", "A221718", "A225546", "A233774", "A233775", "A243071", "A246959", "A265057", "A265058", "A265059", "A265060", "A265061", "A265062", "A265063", "A265064", "A265065", "A265066", "A265067", "A265068", "A265069", "A265070", "A265071", "A265072", "A265073", "A265074", "A265075", "A265076", "A265077", "A362804", "A364289", "A364291", "A364292", "A364295", "A364494", "A364496", "A364497", "A364964", "A365422" ]
[ "M2561" ]
N. J. A. Sloane
2024-08-22T20:35:45
oeisdata/seq/A007/A007283.seq
0a1ea7d3bb7fa6cce56e801d23d2a9e6
A007284
Horizontally symmetric numbers.
[ "0", "1", "3", "8", "10", "11", "13", "18", "30", "31", "33", "38", "80", "81", "83", "88", "100", "101", "103", "108", "110", "111", "113", "118", "130", "131", "133", "138", "180", "181", "183", "188", "300", "301", "303", "308", "310", "311", "313", "318", "330", "331", "333", "338", "380", "381", "383", "388", "800", "801", "803", "808", "810", "811", "813", "818" ]
[ "nonn", "easy", "base" ]
25
0
3
[ "A007284", "A046031" ]
[ "M4477" ]
N. J. A. Sloane.
2020-04-03T04:06:20
oeisdata/seq/A007/A007284.seq
9cf5f194c9592fc8b40810a5f13fe965
A007285
Minimum diameter of an integral set of n points in the plane, not all on a line.
[ "1", "4", "7", "8", "17", "21", "29", "40", "51", "63", "74", "91", "104", "121", "134", "153", "164", "196", "212", "228", "244", "272", "288", "319", "332", "364", "396", "437", "464", "494", "524", "553", "578", "608", "642", "667", "692", "754", "816", "897", "959", "1026", "1066", "1139", "1190", "1248", "1306", "1363" ]
[ "nonn", "nice" ]
32
3
2
[ "A007285", "A096872", "A096873" ]
[ "M3295" ]
N. J. A. Sloane
2023-11-29T11:41:44
oeisdata/seq/A007/A007285.seq
3345269a2feb2f56fa74286360d90195
A007286
E.g.f.: (sin x + cos 2x) / cos 3x.
[ "1", "1", "5", "26", "205", "1936", "22265", "297296", "4544185", "78098176", "1491632525", "31336418816", "718181418565", "17831101321216", "476768795646785", "13658417358350336", "417370516232719345", "13551022195053101056" ]
[ "nonn" ]
48
0
3
[ "A002438", "A006873", "A007286", "A007289", "A225109" ]
[ "M3945" ]
N. J. A. Sloane and Simon Plouffe
2020-03-15T14:17:59
oeisdata/seq/A007/A007286.seq
6a126cdfc9e291836f3cfc8f8fd98a58
A007287
Expansion of layer susceptibility series for cubic lattice.
[ "1", "5", "21", "93", "409", "1837", "8209", "36969", "166041", "748889", "3373941", "15248153", "68840633" ]
[ "nonn" ]
7
0
2
null
[ "M3915" ]
Simon Plouffe
2012-03-30T18:36:11
oeisdata/seq/A007/A007287.seq
21ceabde0567e5bb759006516b029c42
A007288
Expansion of layer susceptibility series for square lattice.
[ "1", "3", "7", "19", "49", "127", "321", "813", "2041", "5117", "12763", "31791", "78917", "195677", "483997", "1196081", "2950439", "7271905" ]
[ "nonn", "more" ]
11
0
2
[ "A007287", "A007288" ]
[ "M2672" ]
Simon Plouffe
2022-02-16T10:26:34
oeisdata/seq/A007/A007288.seq
d48df046e5262a08d806eaa01dc16e5e
A007289
Expansion of e.g.f. (sin 2x + cos x) / cos 3x.
[ "1", "2", "8", "46", "352", "3362", "38528", "515086", "7869952", "135274562", "2583554048", "54276473326", "1243925143552", "30884386347362", "825787662368768", "23657073914466766", "722906928498737152", "23471059057478981762", "806875574817679474688", "29279357851856595135406" ]
[ "nonn" ]
70
0
2
[ "A000191", "A000436", "A006873", "A007286", "A007289", "A225109", "A349271" ]
[ "M1873" ]
N. J. A. Sloane and Simon Plouffe
2024-11-01T13:06:45
oeisdata/seq/A007/A007289.seq
5cd77255c126bf469afa0574ec948717
A007290
a(n) = 2*binomial(n,3).
[ "0", "0", "0", "2", "8", "20", "40", "70", "112", "168", "240", "330", "440", "572", "728", "910", "1120", "1360", "1632", "1938", "2280", "2660", "3080", "3542", "4048", "4600", "5200", "5850", "6552", "7308", "8120", "8990", "9920", "10912", "11968", "13090", "14280", "15540", "16872", "18278", "19760", "21320", "22960", "24682", "26488", "28380", "30360", "32430", "34592", "36848", "39200" ]
[ "nonn", "easy" ]
226
0
4
[ "A000292", "A002378", "A007290", "A008291", "A051925", "A059419", "A074650", "A145066", "A145067", "A145068", "A210569" ]
[ "M1831" ]
N. J. A. Sloane, Simon Plouffe
2024-08-03T01:49:12
oeisdata/seq/A007/A007290.seq
f8294bffb2f644fcf2fd0efbbcddea33
A007291
Series expansion for rectilinear polymers on square lattice.
[ "7", "63", "254", "710", "1605", "3157", "5628", "9324", "14595", "21835", "31482", "44018", "59969", "79905", "104440", "134232", "169983", "212439", "262390", "320670", "388157", "465773", "554484", "655300", "769275", "897507", "1041138", "1201354", "1379385" ]
[ "nonn", "easy" ]
16
2
1
null
[ "M4440" ]
Simon Plouffe
2022-10-21T21:26:44
oeisdata/seq/A007/A007291.seq
734ea8ef1d02dd4276fca7d04602222a
A007292
Number of letters in n (in Hungarian).
[ "5", "2", "5", "5", "3", "2", "3", "3", "4", "6", "3", "7", "10", "10", "8", "7", "8", "8", "9", "11", "3", "7", "10", "10", "8", "7", "8", "8", "9", "11", "7", "9", "12", "12", "10", "9", "10", "10", "11", "13", "6", "8", "11", "11", "9", "8", "9", "9", "10", "12", "5", "7", "10", "10", "8", "7", "8", "8", "9", "11", "6", "8", "11", "11", "9", "8", "9", "9", "10", "12", "6", "8", "11", "11", "9", "8", "9", "9", "10", "12", "7", "9", "12", "12", "10", "9", "10", "10", "11", "13", "9", "11", "14", "14", "12", "11", "12", "12", "13", "15" ]
[ "word", "nonn" ]
27
0
1
null
[ "M1315" ]
N. J. A. Sloane.
2025-02-02T20:12:49
oeisdata/seq/A007/A007292.seq
306ffa9bbac599500b4e4a8a6772b5cf
A007293
Dimension of space of weight systems of chord diagrams.
[ "1", "0", "1", "1", "3", "4", "9", "14", "27", "44", "80", "132", "232" ]
[ "nonn", "more" ]
35
0
5
[ "A007293", "A007473", "A007478", "A014596" ]
[ "M2356" ]
N. J. A. Sloane
2021-12-26T21:38:39
oeisdata/seq/A007/A007293.seq
424e14162f0066e737177835fc163e7a
A007294
Number of partitions of n into nonzero triangular numbers.
[ "1", "1", "1", "2", "2", "2", "4", "4", "4", "6", "7", "7", "10", "11", "11", "15", "17", "17", "22", "24", "25", "32", "35", "36", "44", "48", "50", "60", "66", "68", "81", "89", "92", "107", "117", "121", "141", "153", "159", "181", "197", "205", "233", "252", "262", "295", "320", "332", "372", "401", "417", "465", "501", "520", "575", "619", "645", "710", "763" ]
[ "nonn" ]
125
0
4
[ "A000217", "A000294", "A007294", "A007862", "A024940", "A025487", "A051533", "A102462", "A176723", "A176724", "A179255", "A179269", "A240026", "A280366", "A319797", "A320509", "A325324", "A325354", "A325356", "A325362", "A325363" ]
[ "M0234" ]
N. J. A. Sloane, Mira Bernstein
2024-07-15T12:21:10
oeisdata/seq/A007/A007294.seq
5e0577a59f17b1b08c7851d81f670a59
A007295
Number of elements (a b, c d) in GL(2,Z) with |det| = 1, trace <= n and 0 <= a <= {b, c} <= d.
[ "1", "2", "4", "8", "11", "18", "22", "30", "36", "48", "53", "67", "74", "87", "100", "120", "125", "145", "155", "179", "193", "215", "227", "255", "273", "303", "317", "339", "356", "404", "416", "444", "463", "506", "525", "567", "592", "624", "647", "707", "725", "769", "797", "833", "866", "904", "928", "1008", "1026", "1086", "1125", "1171", "1189", "1247", "1283" ]
[ "nonn" ]
5
1
2
[ "A006546", "A007104", "A007203", "A007295" ]
null
John Lewis (frc.mass.edu)
2020-01-01T16:57:07
oeisdata/seq/A007/A007295.seq
7a3b45862d4227e295c7727c6fcbf6db
A007296
Reversion of (1 + g.f. for primes).
[ "1", "-2", "5", "-15", "52", "-200", "827", "-3596", "16191", "-74702", "350794", "-1669439", "8029728", "-38963552", "190499461", "-937550897", "4641253152", "-23096403422", "115475977145", "-579799302750", "2922325238788", "-14780595276064", "74995317703482", "-381625745964018", "1947147485751919" ]
[ "sign", "easy" ]
26
1
2
[ "A007296", "A334263" ]
[ "M1483" ]
N. J. A. Sloane, Mira Bernstein
2022-10-05T04:58:23
oeisdata/seq/A007/A007296.seq
d3d9f5c1a70e198f3e29dc1cce3f53a3
A007297
Number of connected graphs on n labeled nodes on a circle with straight-line edges that don't cross.
[ "1", "1", "4", "23", "156", "1162", "9192", "75819", "644908", "5616182", "49826712", "448771622", "4092553752", "37714212564", "350658882768", "3285490743987", "30989950019532", "294031964658430", "2804331954047160", "26870823304476690", "258548658860327880" ]
[ "nonn", "easy", "nice" ]
140
1
3
[ "A000108", "A000290", "A001006", "A001187", "A007297", "A054726", "A054921", "A089434", "A099947", "A107111", "A162395", "A194560", "A263843", "A293510", "A323818", "A324167", "A324169", "A324173" ]
[ "M3594" ]
N. J. A. Sloane, Mira Bernstein
2023-10-29T21:51:20
oeisdata/seq/A007/A007297.seq
0e5c56a7cfeecc8ef75274feb542e95f
A007298
Sums of consecutive Fibonacci numbers.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "11", "12", "13", "16", "18", "19", "20", "21", "26", "29", "31", "32", "33", "34", "42", "47", "50", "52", "53", "54", "55", "68", "76", "81", "84", "86", "87", "88", "89", "110", "123", "131", "136", "139", "141", "142", "143", "144", "178", "199", "212", "220", "225", "228", "230", "231", "232", "233", "288", "322" ]
[ "nonn", "easy" ]
30
1
3
[ "A000045", "A007298", "A050939", "A113188", "A219114" ]
null
N. J. A. Sloane, Jan 02 2000
2023-11-16T08:45:18
oeisdata/seq/A007/A007298.seq
f99183bbd215e79fd3605ace30d1c8ed
A007299
Number of Hadamard matrices of order 4n.
[ "1", "1", "1", "1", "5", "3", "60", "487", "13710027" ]
[ "hard", "nonn", "nice" ]
85
0
5
[ "A003432", "A007299", "A019442", "A036297", "A048615", "A048616", "A048885", "A096201" ]
[ "M3736" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A007/A007299.seq
68f2301af689c994bc314b91941d6e49
A007300
a(1)=2, a(2)=5; for n >= 3, a(n) is smallest number which is uniquely of the form a(j) + a(k) with 1 <= j < k < n.
[ "2", "5", "7", "9", "11", "12", "13", "15", "19", "23", "27", "29", "35", "37", "41", "43", "45", "49", "51", "55", "61", "67", "69", "71", "79", "83", "85", "87", "89", "95", "99", "107", "109", "119", "131", "133", "135", "137", "139", "141", "145", "149", "153", "155", "161", "163", "167", "169", "171", "175", "177", "181", "187", "193", "195", "197", "205", "209", "211", "213", "215" ]
[ "nonn", "easy" ]
46
1
1
[ "A003664", "A003666", "A003667", "A006844", "A007300", "A100729" ]
[ "M1328" ]
N. J. A. Sloane, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007300.seq
f56966d01a370d0baddcd5d926774133