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oeis

Dataset card Data Studio Files
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A003201
Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected).
[ "1", "8", "32", "108", "348", "1068", "3180", "9216", "26452", "73708", "206872", "563200", "1555460", "4124568", "11450284" ]
[ "nonn", "more" ]
29
0
2
[ "A003197", "A003198", "A003199", "A003200", "A003201", "A003202", "A003203", "A003204", "A003205", "A003206", "A003207", "A003208", "A003209", "A003210", "A003211", "A003212", "A036392", "A036394", "A036402" ]
[ "M4510" ]
N. J. A. Sloane
2023-01-28T15:47:14
oeisdata/seq/A003/A003201.seq
a7773700c6fc0138eaafe6e04abedfa9
A003202
Cluster series for hexagonal lattice.
[ "1", "6", "18", "48", "126", "300", "750", "1686", "4074", "8868", "20892", "44634", "103392", "216348", "499908", "1017780", "2383596", "4648470", "11271102", "20763036", "52671018", "91377918" ]
[ "nonn", "more" ]
34
0
2
[ "A003197", "A003202", "A003203", "A003204" ]
[ "M4117" ]
N. J. A. Sloane
2023-01-28T15:47:18
oeisdata/seq/A003/A003202.seq
bbe83164cf805a8be64da9577deaf879
A003203
Cluster series for square lattice.
[ "1", "4", "12", "24", "52", "108", "224", "412", "844", "1528", "3152", "5036", "11984", "15040", "46512", "34788", "197612", "4036", "929368", "-702592", "4847552", "-7033956", "27903296", "-54403996", "170579740" ]
[ "sign", "more" ]
33
0
2
[ "A001168", "A003198", "A003202", "A003203", "A003204", "A338210" ]
[ "M3433" ]
N. J. A. Sloane
2022-02-02T15:59:09
oeisdata/seq/A003/A003203.seq
bac1f104f936f11b3d52a7b227e7e22e
A003204
Cluster series for honeycomb.
[ "1", "3", "6", "12", "24", "33", "60", "99", "156", "276", "438", "597", "1134", "1404", "2904", "3522", "6876", "7548", "16680", "18153", "39846", "41805" ]
[ "nonn", "more" ]
23
0
2
[ "A001420", "A003199", "A003202", "A003203", "A003204" ]
[ "M2557" ]
N. J. A. Sloane
2022-02-01T15:07:52
oeisdata/seq/A003/A003204.seq
aca36960dc8396b9dac30afcae9dceb3
A003205
Cluster series for bond percolation problem on f.c.c. lattice.
[ "1", "22", "234", "2348", "22726", "214642", "1993002", "18266276", "165688208" ]
[ "nonn", "more" ]
19
0
2
[ "A003205", "A003206", "A003207", "A003209" ]
[ "M5124" ]
N. J. A. Sloane
2022-02-02T23:57:04
oeisdata/seq/A003/A003205.seq
75c668a63652ea6be89957723d438a8d
A003206
Cluster series for bond percolation problem on b.c.c. lattice.
[ "1", "14", "98", "650", "4202", "26162", "163154", "984104", "6015512", "35540288" ]
[ "nonn", "more" ]
19
0
2
[ "A003205", "A003206", "A003207", "A003210" ]
[ "M4937" ]
N. J. A. Sloane
2022-02-02T23:57:11
oeisdata/seq/A003/A003206.seq
b6116f2e37b7448ccb59fb96fbbbe28e
A003207
Cluster series for bond percolation problem on cubic lattice.
[ "1", "10", "50", "238", "1114", "4998", "22562", "98174", "434894", "1855346", "8125390", "34149330" ]
[ "nonn", "more" ]
16
0
2
[ "A003198", "A003207", "A003211" ]
[ "M4708" ]
N. J. A. Sloane
2022-02-02T23:57:23
oeisdata/seq/A003/A003207.seq
4e526955a1c3db68d1db535a8f7b1fc2
A003208
Cluster series for bond percolation problem on diamond.
[ "1", "6", "18", "54", "162", "456", "1302", "3630", "10158", "27648", "77022", "206508", "570072", "1521822" ]
[ "nonn", "more" ]
18
0
2
[ "A003205", "A003206", "A003207", "A003208", "A003212" ]
[ "M4122" ]
N. J. A. Sloane
2022-02-02T09:00:19
oeisdata/seq/A003/A003208.seq
2f892b5b3fa013097cff8c96521ca696
A003209
Cluster series for f.c.c. lattice.
[ "1", "12", "84", "504", "3012", "17142", "96228", "532028", "2918388", "15763956" ]
[ "nonn", "more" ]
19
0
2
null
[ "M4853" ]
N. J. A. Sloane
2023-10-21T16:58:30
oeisdata/seq/A003/A003209.seq
25d72a092bb3d0416ac6d3a49b67cb5b
A003210
Cluster series for b.c.c. lattice.
[ "1", "8", "56", "248", "1232", "5690", "26636", "113552", "532736", "2207108", "10385062" ]
[ "nonn", "more" ]
19
0
2
null
[ "M4542" ]
N. J. A. Sloane
2023-10-21T16:58:58
oeisdata/seq/A003/A003210.seq
f686003387dff3abcd6bf5e605f174c1
A003211
Cluster series for cubic lattice.
[ "1", "6", "30", "114", "438", "1542", "5754", "19574", "71958", "233574", "870666", "2696274", "10375770", "30198116", "122634404", "327024444", "1460721616", "3347244554", "17795165832" ]
[ "nonn", "more" ]
26
0
2
[ "A003207", "A003209", "A003210", "A003211", "A003212" ]
[ "M4192" ]
N. J. A. Sloane
2022-02-02T04:31:00
oeisdata/seq/A003/A003211.seq
98aaabb9a0e0e952276ac653f1325a5f
A003212
Cluster series for diamond.
[ "1", "4", "12", "36", "108", "264", "708", "1668", "4536", "10926", "28416", "67824", "172464", "408484", "1035932" ]
[ "nonn", "more" ]
17
0
2
[ "A003208", "A003209", "A003210", "A003211", "A003212" ]
[ "M3449" ]
N. J. A. Sloane
2022-02-02T08:50:00
oeisdata/seq/A003/A003212.seq
4164c2dc30afc063dc6ca568f27fcd4e
A003213
Number of ways to quarter a 2n X 2n chessboard.
[ "1", "1", "5", "37", "782", "44240" ]
[ "nonn", "more" ]
83
0
3
[ "A003213", "A006067", "A064941", "A257952" ]
[ "M3987" ]
N. J. A. Sloane
2023-09-28T04:15:58
oeisdata/seq/A003/A003213.seq
1d7ab8d5c87e159c2ff2c684f0019936
A003214
Number of binary forests with n nodes.
[ "1", "1", "2", "3", "6", "10", "20", "37", "76", "152", "320", "672", "1454", "3154", "6959", "15439", "34608", "77988", "176985", "403510", "924683", "2127335", "4913452", "11385955", "26468231", "61700232", "144206269", "337837221", "793213550", "1866181155", "4398867672", "10387045476", "24567374217", "58196129468", "138056734916" ]
[ "nonn", "easy", "nice" ]
36
0
3
[ "A001190", "A003214" ]
[ "M0775" ]
N. J. A. Sloane
2023-09-02T18:52:34
oeisdata/seq/A003/A003214.seq
e158d0d437fd1b16cba748804dc7237d
A003215
Hex (or centered hexagonal) numbers: 3*n*(n+1)+1 (crystal ball sequence for hexagonal lattice).
[ "1", "7", "19", "37", "61", "91", "127", "169", "217", "271", "331", "397", "469", "547", "631", "721", "817", "919", "1027", "1141", "1261", "1387", "1519", "1657", "1801", "1951", "2107", "2269", "2437", "2611", "2791", "2977", "3169", "3367", "3571", "3781", "3997", "4219", "4447", "4681", "4921", "5167", "5419", "5677", "5941", "6211", "6487", "6769" ]
[ "nonn", "easy", "nice" ]
436
0
2
[ "A000124", "A000166", "A000217", "A000290", "A000384", "A000578", "A001263", "A001498", "A001844", "A002061", "A002378", "A002407", "A003215", "A003514", "A005408", "A005448", "A005449", "A005891", "A008292", "A028896", "A045943", "A047969", "A048766", "A056105", "A056106", "A056107", "A056108", "A056109", "A056220", "A060544", "A063496", "A080853", "A130298", "A132111", "A140091", "A154105", "A158405", "A215630", "A220083", "A239449", "A243201", "A287326" ]
[ "M4362" ]
N. J. A. Sloane
2025-03-09T05:10:30
oeisdata/seq/A003/A003215.seq
66f3f6602e2a9da79a514be47a6d1fab
A003216
Number of Hamiltonian graphs with n nodes.
[ "1", "0", "1", "3", "8", "48", "383", "6196", "177083", "9305118", "883156024", "152522187830", "48322518340547" ]
[ "nonn", "nice", "hard", "more" ]
56
1
4
[ "A000088", "A003216", "A006125", "A057864", "A246446", "A283420", "A325447", "A325455", "A326208", "A326215", "A326225", "A326226" ]
[ "M2764" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003216.seq
33543479cac052f234588b9fe521ea1e
A003217
Maximum of minimum total weight for threshold functions of n Boolean variables.
[ "0", "1", "3", "5", "9", "17", "35", "79", "209" ]
[ "nonn", "hard", "more" ]
15
0
3
null
[ "M2455" ]
N. J. A. Sloane
2023-10-21T16:59:46
oeisdata/seq/A003/A003217.seq
f911610204d868afa0b284885e89a9f0
A003218
Weights of threshold functions.
[ "1", "2", "3", "5", "9", "18", "42" ]
[ "nonn" ]
24
2
2
null
[ "M0719" ]
N. J. A. Sloane
2023-10-21T17:06:12
oeisdata/seq/A003/A003218.seq
5950efb132de12111cfbe06769a502aa
A003219
Self numbers divisible by sum of their digits (or, self numbers which are also Harshad numbers).
[ "1", "3", "5", "7", "9", "20", "42", "108", "110", "132", "198", "209", "222", "266", "288", "312", "378", "400", "468", "512", "558", "648", "738", "782", "804", "828", "918", "1032", "1098", "1122", "1188", "1212", "1278", "1300", "1368", "1458", "1526", "1548", "1638", "1704", "1728", "1818", "1974", "2007", "2022", "2088", "2112", "2156", "2178" ]
[ "nonn", "base" ]
22
1
2
[ "A003052", "A003219", "A005349" ]
[ "M2405" ]
N. J. A. Sloane
2023-10-21T17:02:57
oeisdata/seq/A003/A003219.seq
36f544fcd71a9ff0c3bb6fb84c99d86c
A003220
Low-temperature series for spin-1/2 Ising ferromagnetic susceptibility on diamond.
[ "0", "0", "1", "8", "44", "208", "984", "4584", "21314", "98292", "448850", "2038968", "9220346", "41545564", "186796388", "838623100" ]
[ "nonn", "more" ]
23
0
4
[ "A002924", "A002925", "A002926", "A002930", "A003119", "A003220", "A007216" ]
[ "M4530" ]
N. J. A. Sloane, Simon Plouffe
2024-11-15T09:03:38
oeisdata/seq/A003/A003220.seq
ed4c73e70ee7b62d8f2d087c26fcf77f
A003221
Number of even permutations of length n with no fixed points.
[ "1", "0", "0", "2", "3", "24", "130", "930", "7413", "66752", "667476", "7342290", "88107415", "1145396472", "16035550518", "240533257874", "3848532125865", "65425046139840", "1177650830516968", "22375365779822562", "447507315596451051", "9397653627525472280", "206748379805560389930" ]
[ "nonn", "easy", "nice" ]
56
0
4
[ "A000166", "A000387", "A003221" ]
[ "M0922" ]
N. J. A. Sloane
2020-02-11T19:52:24
oeisdata/seq/A003/A003221.seq
5118fa3740ead940e50295eb38311705
A003222
a(n) = 2^(3*n+1) - 2*n*(2*n+1).
[ "2", "10", "108", "982", "8120", "65426", "524132", "4194094", "33554160", "268435114", "2147483228", "17179868678", "137438952872", "1099511627074", "8796093021396", "70368744176734", "562949953420256", "4503599627369306", "36028797018962636", "288230376151710262", "2305843009213692312", "18446744073709549810" ]
[ "nonn", "easy" ]
31
0
1
[ "A002943", "A003222", "A013730" ]
null
N. J. A. Sloane
2025-03-06T20:29:10
oeisdata/seq/A003/A003222.seq
122253ee5884c68f8b5aff400ca33cbb
A003223
Erroneous version of A006841.
[ "1", "2", "4", "10", "28", "130" ]
[ "dead" ]
26
3
2
[ "A003223", "A003224", "A003225", "A006841" ]
[ "M1226" ]
N. J. A. Sloane
2023-10-21T17:04:04
oeisdata/seq/A003/A003223.seq
b8ce55805babfb0f0d1358d2a995fbea
A003224
The number of superpositions of cycles of order n of the groups E_3 and D_n.
[ "1", "5", "24", "391", "9549", "401547", "22597671", "1646431048", "149640359575", "16597459048676", "2206178465445432", "346212403086248325", "63333787189956042080", "13359470726804093346852", "3218846593376516669825536", "878566295178157438213870011" ]
[ "nonn", "easy" ]
21
3
2
[ "A000940", "A003224", "A003225", "A006841" ]
[ "M3934" ]
N. J. A. Sloane
2023-10-21T17:04:59
oeisdata/seq/A003/A003224.seq
a64d331ba7939f0f9e49a7d6ee99455d
A003225
The number of superpositions of cycles of order n of the groups S_3 and D_n.
[ "1", "3", "9", "89", "1705", "67750", "3771993", "274460137", "24940556932", "2766249007425", "367696475451179", "57702068070938071", "10555631209951650809", "2226578454651253107758", "536474432232188713033347", "146427715863075641229151764", "44945602048024898356307332914" ]
[ "nonn", "easy" ]
21
3
2
[ "A003224", "A003225", "A006841" ]
[ "M2827" ]
N. J. A. Sloane
2023-10-21T17:05:35
oeisdata/seq/A003/A003225.seq
cfbdd0e0c8ef80c813b237ed5a1af13a
A003226
Automorphic numbers: m^2 ends with m.
[ "0", "1", "5", "6", "25", "76", "376", "625", "9376", "90625", "109376", "890625", "2890625", "7109376", "12890625", "87109376", "212890625", "787109376", "1787109376", "8212890625", "18212890625", "81787109376", "918212890625", "9918212890625", "40081787109376", "59918212890625", "259918212890625", "740081787109376" ]
[ "nonn", "base", "nice", "easy" ]
173
1
3
[ "A003226", "A008851", "A018247", "A018248", "A018834", "A033819", "A035383", "A046831", "A052228" ]
[ "M3752" ]
N. J. A. Sloane
2025-03-14T17:26:14
oeisdata/seq/A003/A003226.seq
c3293e803cd230605e0db7e3445334be
A003227
Endpoints (leaves) in rooted trees with n nodes.
[ "1", "1", "3", "8", "22", "58", "160", "434", "1204", "3341", "9363", "26308", "74376", "210823", "599832", "1710803", "4891876", "14015505", "40231632", "115669419", "333052242", "960219982", "2771707332", "8009222307", "23166563032", "67069289457", "194332834601" ]
[ "nonn" ]
33
1
3
[ "A000081", "A003227", "A003228", "A004111", "A038046", "A055277", "A317580" ]
[ "M2744" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003227.seq
3cacb04151c5d95f17446ae43fb44338
A003228
Endpoints in trees with n nodes.
[ "1", "2", "2", "5", "9", "21", "43", "101", "226", "556", "1333", "3365", "8500", "22007", "57258", "151264", "401761", "1077063", "2902599", "7871250", "21440642", "58672589", "161155637", "444240627", "1228400744", "3406668865", "9472308269", "26402207803", "73755064178" ]
[ "nonn" ]
26
1
2
[ "A000055", "A003227", "A003228", "A055290", "A055372" ]
[ "M0351" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003228.seq
81ee03ba7cd7294e2da6114145f9e937
A003229
a(n) = a(n-1) + 2*a(n-3) with a(0)=a(1)=1, a(2)=3.
[ "1", "1", "3", "5", "7", "13", "23", "37", "63", "109", "183", "309", "527", "893", "1511", "2565", "4351", "7373", "12503", "21205", "35951", "60957", "103367", "175269", "297183", "503917", "854455", "1448821", "2456655", "4165565", "7063207", "11976517", "20307647", "34434061", "58387095", "99002389" ]
[ "nonn", "easy" ]
107
0
3
[ "A003229", "A003230", "A003479", "A052537", "A077906", "A077949", "A077974", "A155761" ]
[ "M2419" ]
N. J. A. Sloane
2024-08-01T03:03:24
oeisdata/seq/A003/A003229.seq
450f96b7e319485bf453f9fe5a7de84b
A003230
Expansion of 1/((1-x)*(1-2*x)*(1-x-2*x^3)).
[ "1", "4", "11", "28", "67", "152", "335", "724", "1539", "3232", "6727", "13900", "28555", "58392", "118959", "241604", "489459", "989520", "1997015", "4024508", "8100699", "16289032", "32726655", "65705268", "131837763", "264399936", "530028199", "1062139180", "2127809963" ]
[ "nonn", "easy" ]
96
0
2
[ "A003229", "A003230", "A003477", "A077949" ]
[ "M3417" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A003/A003230.seq
272c75b0fb681ff80d9a1ba0d47b61e3
A003231
a(n) = floor(n*(sqrt(5)+5)/2).
[ "3", "7", "10", "14", "18", "21", "25", "28", "32", "36", "39", "43", "47", "50", "54", "57", "61", "65", "68", "72", "75", "79", "83", "86", "90", "94", "97", "101", "104", "108", "112", "115", "119", "123", "126", "130", "133", "137", "141", "144", "148", "151", "155", "159", "162", "166", "170", "173", "177", "180", "184", "188", "191", "195", "198", "202", "206", "209" ]
[ "nonn", "easy" ]
69
1
1
[ "A000201", "A003231", "A003233", "A003234", "A105424", "A249115", "A362917" ]
[ "M2618" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003231.seq
787176a8af18654d8f26e99f14dc2512
A003232
Expansion of (x-1)*(x^2-4*x-1)/(1-2*x)^2.
[ "1", "7", "19", "49", "120", "284", "656", "1488", "3328", "7360", "16128", "35072", "75776", "162816", "348160", "741376", "1572864", "3325952", "7012352", "14745600", "30932992", "64749568", "135266304", "282066944", "587202560", "1220542464" ]
[ "nonn" ]
8
0
2
null
null
N. J. A. Sloane
2023-10-21T17:10:13
oeisdata/seq/A003/A003232.seq
2eb2a3e4b7a7e6a04e20c8511f390968
A003233
Numbers k such that A003231(A001950(k)) = A001950(A003231(k)).
[ "1", "2", "4", "5", "6", "7", "9", "10", "12", "13", "14", "15", "17", "18", "20", "22", "23", "25", "26", "27", "28", "30", "31", "33", "34", "35", "36", "38", "39", "40", "41", "43", "44", "46", "47", "48", "49", "51", "52", "54", "56", "57", "59", "60", "61", "62", "64", "65", "67", "68", "69", "70", "72", "73", "75", "77", "78", "80", "81", "82", "83", "85", "86", "88", "89", "90", "91" ]
[ "nonn" ]
41
1
2
[ "A001950", "A003231", "A003233", "A003234" ]
[ "M0944" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003233.seq
9e28e8c1c626e2fa749e8b5a6c3b1c6b
A003234
Numbers k such that A003231(A001950(k)) = A001950(A003231(k)) - 1.
[ "3", "8", "11", "16", "19", "21", "24", "29", "32", "37", "42", "45", "50", "53", "55", "58", "63", "66", "71", "74", "76", "79", "84", "87", "92", "97", "100", "105", "108", "110", "113", "118", "121", "126", "129", "131", "134", "139", "142", "144", "147", "152", "155", "160", "163", "165", "168", "173", "176", "181", "186", "189", "194", "197", "199", "202", "207" ]
[ "nonn" ]
42
1
1
[ "A001950", "A003231", "A003234" ]
[ "M2714" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003234.seq
a573f14a8103b56f06347e1ccd041eef
A003235
a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k)*C(k^2,n).
[ "1", "1", "6", "72", "1322", "32550", "1003632", "37162384", "1605962556", "79330914540", "4409098539560", "272297452742304", "18499002436677336", "1371050716542451672", "110085169034456183232", "9519063815009322326400", "881914870734754844035088", "87154631117420724492647184" ]
[ "nonn" ]
33
0
3
[ "A003235", "A346184" ]
[ "M4280" ]
N. J. A. Sloane
2021-07-09T17:34:18
oeisdata/seq/A003/A003235.seq
2c2701dd7e158b3dbdc910ca90d2b60f
A003236
a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k)*C((k+1)^2, n).
[ "1", "3", "24", "320", "6122", "153762", "4794664", "178788528", "7762727196", "384733667780", "21434922419504", "1326212860090560", "90227121642144424", "6694736236093168200", "538028902298395832832", "46558260925421295229568", "4316186393637505403773328" ]
[ "nonn" ]
33
0
2
[ "A003236", "A346183" ]
[ "M3107" ]
N. J. A. Sloane
2021-12-26T20:41:30
oeisdata/seq/A003/A003236.seq
3b5958fc63b8d052378fc16fd511f0fe
A003237
Number of partially achiral planted trees with n nodes.
[ "0", "0", "1", "1", "2", "3", "6", "10", "19", "33", "62", "110", "204", "366", "677", "1223", "2254", "4089", "7526", "13692", "25171", "45882", "84291", "153860", "282509", "516192", "947469", "1732477", "3179083", "5816301", "10670751", "19531034", "35826689", "65596323", "120312363", "220340374", "404096665", "740212002", "1357426934" ]
[ "nonn" ]
45
0
5
null
[ "M0766" ]
N. J. A. Sloane
2023-10-21T17:11:37
oeisdata/seq/A003/A003237.seq
8f7f1de25d865599e9543867bd00cb30
A003238
Number of rooted trees with n vertices in which vertices at the same level have the same degree.
[ "1", "1", "2", "3", "5", "6", "10", "11", "16", "19", "26", "27", "40", "41", "53", "61", "77", "78", "104", "105", "134", "147", "175", "176", "227", "233", "275", "294", "350", "351", "438", "439", "516", "545", "624", "640", "774", "775", "881", "924", "1069", "1070", "1265", "1266", "1444", "1521", "1698", "1699" ]
[ "nonn", "nice", "eigen" ]
124
1
3
[ "A000123", "A002033", "A003238", "A004111", "A007439", "A007554", "A027750", "A051731", "A057546", "A122934", "A152434", "A280994", "A281487" ]
[ "M0628" ]
N. J. A. Sloane
2024-12-06T20:18:45
oeisdata/seq/A003/A003238.seq
a1c9b2f663e95f609b5a53d8a1b1a705
A003239
Number of rooted planar trees with n non-root nodes: circularly cycling the subtrees at the root gives equivalent trees.
[ "1", "1", "2", "4", "10", "26", "80", "246", "810", "2704", "9252", "32066", "112720", "400024", "1432860", "5170604", "18784170", "68635478", "252088496", "930138522", "3446167860", "12815663844", "47820447028", "178987624514", "671825133648", "2528212128776", "9536895064400", "36054433810102", "136583761444364", "518401146543812" ]
[ "nonn", "nice", "easy" ]
140
0
3
[ "A000108", "A002995", "A003239", "A022553", "A037306", "A057510", "A082936", "A084575", "A208183", "A261494" ]
[ "M1222" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003239.seq
69c290425cf91559295c0eef47b40ab8
A003240
Number of partially achiral rooted trees.
[ "1", "1", "2", "4", "8", "16", "31", "62", "120", "236", "454", "884", "1697", "3275", "6266", "12020", "22935", "43788", "83325", "158516", "300914", "570794", "1081157", "2045934", "3867617", "7304149", "13783221", "25984936", "48956715", "92155376", "173376484", "325919786", "612378787", "1149777034" ]
[ "nonn", "easy" ]
31
1
3
null
[ "M1123" ]
N. J. A. Sloane
2024-11-21T20:08:49
oeisdata/seq/A003/A003240.seq
48e64cdbefe422f8d8108137fd7df34b
A003241
Number of achiral rooted trees.
[ "1", "1", "2", "4", "8", "15", "26", "45", "71", "110", "168", "247", "351", "503", "700", "944", "1294", "1719", "2267", "2961", "3839", "4891", "6297", "7891", "9912", "12347", "15381", "18784", "23203", "28138", "34233", "41275", "49824", "59306", "71309", "84268", "100127", "118045", "139472", "162659" ]
[ "nonn" ]
32
1
3
null
[ "M1101" ]
N. J. A. Sloane
2020-04-07T11:07:27
oeisdata/seq/A003/A003241.seq
a2dfb9c99e07d42088bf65cc123a0bb4
A003242
Number of compositions of n such that no two adjacent parts are equal (these are sometimes called Carlitz compositions).
[ "1", "1", "1", "3", "4", "7", "14", "23", "39", "71", "124", "214", "378", "661", "1152", "2024", "3542", "6189", "10843", "18978", "33202", "58130", "101742", "178045", "311648", "545470", "954658", "1670919", "2924536", "5118559", "8958772", "15680073", "27443763", "48033284", "84069952", "147142465", "257534928", "450748483", "788918212" ]
[ "nonn", "nice" ]
126
0
4
[ "A000740", "A003242", "A005251", "A011782", "A032020", "A048272", "A096568", "A106351", "A106356", "A114900", "A114901", "A114902", "A167606", "A178470", "A232396", "A241701", "A241902", "A261041", "A261960", "A261983", "A274174", "A329738", "A329863" ]
null
E. Rodney Canfield
2025-01-05T19:51:33
oeisdata/seq/A003/A003242.seq
58a2aee72e9c7ae902a85b4b92763c33
A003243
Number of partially achiral trees with n nodes.
[ "1", "1", "1", "2", "3", "6", "9", "19", "30", "61", "99", "198", "333", "650", "1115", "2143", "3743", "7101", "12553", "23605", "42115", "78670", "141284", "262679", "474083", "878386", "1591038", "2940512", "5340712", "9852201", "17930619", "33031498", "60209609", "110801271", "202208576", "371820314" ]
[ "nonn", "easy" ]
37
1
4
null
[ "M0760" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A003/A003243.seq
f1144f7520d40a42d8d717abbf1c18e9
A003244
Number of unrooted achiral trees with n nodes.
[ "1", "1", "1", "2", "3", "6", "9", "16", "23", "35", "51", "72", "97", "136", "186", "230", "321", "401", "526", "647", "844", "1000", "1331", "1539", "1960", "2299", "2943", "3307", "4237", "4779", "5961", "6744", "8372", "9239", "11605", "12694", "15549", "17264", "21086", "22784", "27976", "30357", "36598", "39843", "47821" ]
[ "nonn", "easy" ]
27
1
4
null
[ "M0759" ]
N. J. A. Sloane
2017-06-26T22:39:34
oeisdata/seq/A003/A003244.seq
299144af0a0a9e8c1eb7f0c36f80b2c2
A003245
Nearest integer to -4n/Bernoulli(2n).
[ "0", "-24", "240", "-504", "480", "-264", "95", "-24", "5", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
17
0
2
[ "A000367", "A002445", "A003245" ]
null
N. J. A. Sloane
2023-10-21T17:20:43
oeisdata/seq/A003/A003245.seq
20825a451e9705c7dac5756d2b40f58d
A003246
Discriminants of real quadratic norm-Euclidean fields (a finite sequence).
[ "5", "8", "12", "13", "17", "21", "24", "28", "29", "33", "37", "41", "44", "57", "73", "76" ]
[ "fini", "full", "nonn", "nice" ]
60
1
1
[ "A003174", "A003246", "A003656" ]
[ "M3778" ]
N. J. A. Sloane
2024-08-01T09:24:08
oeisdata/seq/A003/A003246.seq
995b9d393a7682b90c2284b4c5684c7d
A003247
Complement of A003248.
[ "1", "2", "3", "4", "6", "7", "8", "9", "10", "11", "12", "13", "15", "16", "17", "18", "19", "21", "22", "23", "24", "25", "26", "27", "28", "30", "31", "32", "33", "34", "36", "37", "38", "40", "41", "42", "43", "44", "46", "47", "48", "49", "50", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "63", "64", "65", "66", "67", "68", "70", "71", "72", "73", "74", "75", "76", "77" ]
[ "nonn" ]
30
1
2
null
[ "M0539" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003247.seq
d1cae85e174dffbdb8d3d0573858563d
A003248
a(n) = A000201(A003234(n)) + n.
[ "5", "14", "20", "29", "35", "39", "45", "54", "60", "69", "78", "84", "93", "99", "103", "109", "118", "124", "133", "139", "143", "149", "158", "164", "173", "182", "188", "197", "203", "207", "213", "222", "228", "237", "243", "247", "253", "262", "268", "272", "278", "287", "293", "302", "308", "312", "318", "327", "333", "342", "351", "357", "366", "372", "376" ]
[ "nonn" ]
22
1
1
[ "A000201", "A003234", "A003248" ]
[ "M3839" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003248.seq
115993be54637687357f4000cbc59369
A003249
a(n) = A001950(A003234(n)) + 1.
[ "8", "21", "29", "42", "50", "55", "63", "76", "84", "97", "110", "118", "131", "139", "144", "152", "165", "173", "186", "194", "199", "207", "220", "228", "241", "254", "262", "275", "283", "288", "296", "309", "317", "330", "338", "343", "351", "364", "372", "377", "385", "398", "406", "419", "427", "432", "440", "453", "461", "474", "487", "495", "508", "516" ]
[ "nonn" ]
31
1
1
[ "A001950", "A003234", "A003249", "A242094" ]
[ "M4492" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003249.seq
f2a9f7391920e1aab7e5b0617bf1d530
A003250
The number m such that A001950(m) = A003231(A003234(n)).
[ "4", "11", "15", "22", "26", "29", "33", "40", "44", "51", "58", "62", "69", "73", "76", "80", "87", "91", "98", "102", "105", "109", "116", "120", "127", "134", "138", "145", "149", "152", "156", "163", "167", "174", "178", "181", "185", "192", "196", "199", "203", "210", "214", "221", "225", "228", "232", "239", "243", "250", "257", "261", "268", "272", "275", "279" ]
[ "nonn" ]
19
1
1
null
[ "M3405" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003250.seq
64e3ce80fba47e1354c6910d7da9b140
A003251
Complement of A003250.
[ "1", "2", "3", "5", "6", "7", "8", "9", "10", "12", "13", "14", "16", "17", "18", "19", "20", "21", "23", "24", "25", "27", "28", "30", "31", "32", "34", "35", "36", "37", "38", "39", "41", "42", "43", "45", "46", "47", "48", "49", "50", "52", "53", "54", "55", "56", "57", "59", "60", "61", "63", "64", "65", "66", "67", "68", "70", "71", "72", "74", "75", "77", "78", "79", "81", "82", "83" ]
[ "nonn" ]
22
1
2
null
[ "M0612" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003251.seq
fa7eae596014523f3dd54def2abf5188
A003252
The number m such that A003251(m) = A003231(n).
[ "3", "6", "9", "12", "15", "18", "21", "23", "26", "29", "32", "35", "38", "41", "44", "47", "50", "53", "56", "59", "61", "64", "67", "70", "73", "76", "79", "82", "84", "87", "90", "93", "96", "99", "102", "105", "108", "111", "114", "117", "120", "122", "125", "128", "131", "134", "137", "140", "143", "145", "148", "151", "154", "157", "159", "162", "165", "168", "171" ]
[ "nonn" ]
22
1
1
[ "A003252", "A003253" ]
[ "M2521" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003252.seq
1b9d4aede7e21d5378dc7661eb75cbd3
A003253
Complement of A003252.
[ "1", "2", "4", "5", "7", "8", "10", "11", "13", "14", "16", "17", "19", "20", "22", "24", "25", "27", "28", "30", "31", "33", "34", "36", "37", "39", "40", "42", "43", "45", "46", "48", "49", "51", "52", "54", "55", "57", "58", "60", "62", "63", "65", "66", "68", "69", "71", "72", "74", "75", "77", "78", "80", "81", "83", "85", "86", "88", "89", "91", "92", "94", "95", "97", "98", "100" ]
[ "nonn" ]
29
1
2
[ "A001651", "A003252", "A003253" ]
[ "M0958" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003253.seq
5af36d04aa5593781a8115322d9bbdd1
A003254
The number m such that A003233(m) = A005206(A003234(n)).
[ "2", "4", "6", "8", "9", "10", "12", "14", "15", "17", "19", "21", "23", "24", "25", "27", "29", "31", "33", "34", "35", "37", "39", "40", "42", "44", "46", "48", "49", "50", "52", "54", "55", "57", "58", "59", "61", "63", "64", "65", "67", "69", "71", "73", "74", "75", "77", "79", "80", "82", "84", "86", "88", "89", "90", "92", "94", "95", "97", "98", "99", "101", "103", "104", "106" ]
[ "nonn" ]
17
1
1
null
[ "M0984" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003254.seq
761ad529ab6c22997a851f3869869407
A003255
Complement of A003254.
[ "1", "3", "5", "7", "11", "13", "16", "18", "20", "22", "26", "28", "30", "32", "36", "38", "41", "43", "45", "47", "51", "53", "56", "60", "62", "66", "68", "70", "72", "76", "78", "81", "83", "85", "87", "91", "93", "96", "100", "102", "105", "107", "109", "111", "115", "117", "120", "122", "124", "126", "130", "132", "134", "136", "140", "142", "145", "147", "149", "151" ]
[ "nonn" ]
22
1
2
null
[ "M2410" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003255.seq
b11031ac3f770cc92b345375bbfc2de3
A003256
a(n) is the number m such that A242094(m) = A001950(n).
[ "2", "5", "7", "9", "12", "14", "17", "19", "21", "24", "26", "28", "31", "33", "36", "38", "40", "43", "45", "47", "49", "51", "54", "56", "58", "61", "63", "66", "68", "70", "73", "75", "77", "80", "82", "85", "87", "89", "92", "94", "97", "99", "101", "104", "106", "108", "111", "113", "116", "118", "120", "123", "125", "127", "129", "131", "134", "136", "138", "141", "143" ]
[ "nonn" ]
32
1
1
[ "A001950", "A003234", "A003256", "A242094" ]
[ "M1330" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003256.seq
a586e74f1f08d80687328f8ee3736f4a
A003257
Complement of A003256.
[ "1", "3", "4", "6", "8", "10", "11", "13", "15", "16", "18", "20", "22", "23", "25", "27", "29", "30", "32", "34", "35", "37", "39", "41", "42", "44", "46", "48", "50", "52", "53", "55", "57", "59", "60", "62", "64", "65", "67", "69", "71", "72", "74", "76", "78", "79", "81", "83", "84", "86", "88", "90", "91", "93", "95", "96", "98", "100", "102", "103", "105", "107", "109", "110" ]
[ "nonn" ]
18
1
2
null
[ "M2325" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003257.seq
27c68b96509d165aed92633339ef5b04
A003258
The number m such that c'(m) = A005206(A003231(n)), where c'(m) = A249115(m) is the m-th positive integer not in A003231.
[ "2", "3", "5", "7", "8", "10", "12", "13", "15", "16", "18", "20", "21", "23", "24", "26", "28", "29", "31", "33", "34", "36", "37", "39", "41", "42", "44", "46", "47", "49", "50", "52", "54", "55", "57", "58", "60", "62", "63", "65", "67", "68", "70", "71", "73", "75", "76", "78", "80", "81", "83", "84", "86", "88", "89", "91", "92", "94", "96", "97", "99", "101", "102", "104", "105" ]
[ "nonn" ]
25
1
1
null
[ "M0635" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003258.seq
b6256373460210b705550c8d475c5baa
A003259
Complement of A003258.
[ "1", "4", "6", "9", "11", "14", "17", "19", "22", "25", "27", "30", "32", "35", "38", "40", "43", "45", "48", "51", "53", "56", "59", "61", "64", "66", "69", "72", "74", "77", "79", "82", "85", "87", "90", "93", "95", "98", "100", "103", "106", "108", "111", "114", "116", "119", "121", "124", "127", "129", "132", "134", "137", "140", "142", "145", "148", "150", "153", "155" ]
[ "nonn" ]
17
1
2
null
[ "M3276" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003259.seq
749792675e21415979dd5669b0882ed6
A003260
Largest prime factor of n-th Mersenne number (A001348(n)).
[ "3", "7", "31", "127", "89", "8191", "131071", "524287", "178481", "2089", "2147483647", "616318177", "164511353", "2099863", "13264529", "20394401", "3203431780337", "2305843009213693951" ]
[ "nonn", "nice", "changed" ]
62
1
1
[ "A000668", "A001348", "A003260", "A016047", "A046800" ]
[ "M2693" ]
N. J. A. Sloane
2025-04-20T04:07:44
oeisdata/seq/A003/A003260.seq
52c33e9a9dee549740128b8400b7c2b5
A003261
Woodall (or Riesel) numbers: n*2^n - 1.
[ "1", "7", "23", "63", "159", "383", "895", "2047", "4607", "10239", "22527", "49151", "106495", "229375", "491519", "1048575", "2228223", "4718591", "9961471", "20971519", "44040191", "92274687", "192937983", "402653183", "838860799", "1744830463", "3623878655", "7516192767", "15569256447", "32212254719", "66571993087" ]
[ "nonn", "easy", "nice", "changed" ]
141
1
2
[ "A002064", "A002234", "A003261", "A005849", "A006127", "A036289", "A050918", "A133653" ]
[ "M4379" ]
N. J. A. Sloane
2025-04-25T10:28:30
oeisdata/seq/A003/A003261.seq
7c7948510f11f27a6ec7045386f2fdd6
A003262
Let y=f(x) satisfy F(x,y)=0. a(n) is the number of terms in the expansion of (d/dx)^n y in terms of the partial derivatives of F.
[ "1", "3", "9", "24", "61", "145", "333", "732", "1565", "3247", "6583", "13047", "25379", "48477", "91159", "168883", "308736", "557335", "994638", "1755909", "3068960", "5313318", "9118049", "15516710", "26198568", "43904123", "73056724", "120750102", "198304922", "323685343" ]
[ "nonn", "nice", "easy" ]
46
1
2
[ "A003262", "A098504", "A162326", "A172003", "A172004" ]
[ "M2791" ]
N. J. A. Sloane
2023-10-16T03:33:41
oeisdata/seq/A003/A003262.seq
22085499bb3351e5e61242fc6a5201ee
A003263
Number of representations of n as a sum of distinct Lucas numbers 1, 3, 4, 7, 11, ... (A000204).
[ "1", "0", "1", "2", "1", "0", "2", "2", "0", "1", "3", "2", "0", "2", "3", "1", "0", "3", "3", "0", "2", "4", "2", "0", "3", "3", "0", "1", "4", "3", "0", "3", "5", "2", "0", "4", "4", "0", "2", "5", "3", "0", "3", "4", "1", "0", "4", "4", "0", "3", "6", "3", "0", "5", "5", "0", "2", "6", "4", "0", "4", "6", "2", "0", "5", "5", "0", "3", "6", "3", "0", "4", "4", "0", "1", "5", "4", "0", "4", "7", "3", "0", "6", "6", "0", "3", "8", "5", "0", "5", "7", "2", "0", "6", "6", "0", "4", "8", "4", "0", "6", "6", "0", "2", "7" ]
[ "nonn", "easy" ]
35
1
4
[ "A000204", "A003263", "A054770" ]
[ "M0045" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003263.seq
4bfcd46588fafd471ae4f75ce1d35549
A003264
a(n) = floor((-4n)/Bernoulli(2n)).
[ "0", "-24", "240", "-504", "480", "-264", "94", "-24", "4", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1" ]
[ "sign" ]
21
0
2
null
null
N. J. A. Sloane
2023-10-21T23:38:07
oeisdata/seq/A003/A003264.seq
927f258f138ad6cb5a39d4edbd1ce835
A003265
Not representable by truncated tribonacci sequence 2, 4, 7, 13, 24, 44, 81, ....
[ "1", "3", "5", "8", "10", "12", "14", "16", "18", "21", "23", "25", "27", "29", "32", "34", "36", "38", "40", "42", "45", "47", "49", "52", "54", "56", "58", "60", "62", "65", "67", "69", "71", "73", "76", "78", "80", "82", "84", "86", "89", "91", "93", "95", "97", "99", "102", "104", "106", "108", "110", "113", "115", "117", "119", "121", "123" ]
[ "nonn" ]
29
1
2
[ "A000073", "A003265", "A003726", "A136175", "A278038" ]
[ "M2430" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003265.seq
75e44b2ccab138a7e6b9d63ee3b876b5
A003266
Product of first n nonzero Fibonacci numbers F(1), ..., F(n).
[ "1", "1", "1", "2", "6", "30", "240", "3120", "65520", "2227680", "122522400", "10904493600", "1570247078400", "365867569267200", "137932073613734400", "84138564904377984000", "83044763560621070208000", "132622487406311849122176000", "342696507457909818131702784000" ]
[ "nonn", "easy", "nice" ]
118
0
4
[ "A000045", "A002110", "A003046", "A003266", "A069777", "A070825", "A101689", "A123741", "A126772", "A135598", "A158472", "A176343", "A238243", "A238244" ]
[ "M1692" ]
N. J. A. Sloane
2025-03-11T08:41:28
oeisdata/seq/A003/A003266.seq
d8fa49d0de86bcce126eb799b9d8a00c
A003267
Central Fibonomial coefficients.
[ "1", "1", "6", "60", "1820", "136136", "27261234", "14169550626", "19344810307020", "69056421075989160", "645693859487298425256", "15803204856220738696714416", "1012673098498882654470985390406", "169885799961166470686816475170920550", "74614732877610423587753604318734054624100" ]
[ "nonn", "easy" ]
73
0
3
[ "A001622", "A003267", "A003268", "A008341", "A062073", "A062381" ]
[ "M4272" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003267.seq
ff994631f8d3c89823db52927f5fbc14
A003268
Central Fibonomial coefficients.
[ "1", "2", "6", "15", "60", "260", "1820", "12376", "136136", "1514513", "27261234", "488605194", "14169550626", "411591708660", "19344810307020", "908637119420910", "69056421075989160", "5249543573067466872", "645693859487298425256", "79413089729752455762384", "15803204856220738696714416" ]
[ "nonn" ]
26
0
2
[ "A003268", "A010048", "A055870", "A062073" ]
[ "M1607" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003268.seq
ecc3ced326b45fc1aa0e384c6bed8054
A003269
a(n) = a(n-1) + a(n-4) with a(0) = 0, a(1) = a(2) = a(3) = 1.
[ "0", "1", "1", "1", "1", "2", "3", "4", "5", "7", "10", "14", "19", "26", "36", "50", "69", "95", "131", "181", "250", "345", "476", "657", "907", "1252", "1728", "2385", "3292", "4544", "6272", "8657", "11949", "16493", "22765", "31422", "43371", "59864", "82629", "114051", "157422", "217286", "299915", "413966", "571388", "788674", "1088589", "1502555", "2073943" ]
[ "nonn", "easy" ]
280
0
6
[ "A000045", "A000079", "A000930", "A003269", "A003520", "A005708", "A005709", "A005710", "A005711", "A017898", "A048718", "A072827", "A072850", "A072851", "A072852", "A072853", "A072854", "A072855", "A072856", "A079955", "A080014", "A180184" ]
[ "M0526" ]
N. J. A. Sloane
2025-03-21T09:25:51
oeisdata/seq/A003/A003269.seq
f316123221085c47203cbd3011d78082
A003270
A nonrepetitive sequence.
[ "1", "2", "3", "1", "3", "2", "3", "1", "2", "3", "2", "1", "3", "1", "2", "1", "3", "2", "3", "1", "2", "3", "2", "1", "2", "3", "1", "2", "1", "3", "2", "3", "1", "3", "2", "1", "3", "1", "2", "3", "2", "1", "2", "3", "1", "3", "2", "1", "3", "1", "2", "1", "3", "2", "3", "1", "2", "3", "2", "1", "2", "3", "1", "2", "1", "3", "2", "3", "1" ]
[ "nonn" ]
28
1
2
[ "A003270", "A099054" ]
[ "M0407" ]
N. J. A. Sloane
2023-10-22T00:19:20
oeisdata/seq/A003/A003270.seq
a61de6a555976cad630ccf1c80655f52
A003271
Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1.
[ "1", "2", "3", "4", "5", "9", "16", "17", "41", "83", "113", "137", "257", "773", "977", "1657", "2048", "2313", "4001", "5725", "7129", "11117", "17279", "19897", "22409", "39283", "43657", "55457", "120677", "308941", "314521", "465089", "564353", "797931", "1110841", "1310443", "1924159", "2535041", "3637637", "6001937", "8319617", "9453569", "10969369" ]
[ "nonn", "nice", "easy" ]
37
0
2
[ "A003271", "A047994", "A049865", "A225172", "A225173" ]
[ "M0531" ]
N. J. A. Sloane
2017-10-05T17:21:48
oeisdata/seq/A003/A003271.seq
149ceef6ea4c00fb8a6865d2b7e523e0
A003272
a(n) = ceiling((-4n)/Bernoulli(2n)).
[ "0", "-24", "240", "-504", "480", "-264", "95", "-24", "5", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0" ]
[ "sign" ]
20
0
2
null
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A003/A003272.seq
75f6699a5b05d9d97ca4b146e0901f6e
A003273
Congruent numbers: positive integers k for which there exists a right triangle having area k and rational sides.
[ "5", "6", "7", "13", "14", "15", "20", "21", "22", "23", "24", "28", "29", "30", "31", "34", "37", "38", "39", "41", "45", "46", "47", "52", "53", "54", "55", "56", "60", "61", "62", "63", "65", "69", "70", "71", "77", "78", "79", "80", "84", "85", "86", "87", "88", "92", "93", "94", "95", "96", "101", "102", "103", "109", "110", "111", "112", "116", "117", "118", "119", "120", "124", "125", "126" ]
[ "nonn", "nice" ]
143
1
1
[ "A003273", "A006991", "A072068", "A072069", "A072070", "A072071", "A073120", "A165564", "A182429", "A256418", "A259680", "A259687" ]
[ "M3747" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003273.seq
a7e2f23f51c59e9cf69b3ae4d18e7a80
A003274
Number of key permutations of length n: permutations {a_i} with |a_i - a_{i-1}| = 1 or 2.
[ "1", "1", "2", "6", "12", "20", "34", "56", "88", "136", "208", "314", "470", "700", "1038", "1534", "2262", "3330", "4896", "7192", "10558", "15492", "22724", "33324", "48860", "71630", "105002", "153912", "225594", "330650", "484618", "710270", "1040980", "1525660", "2235994", "3277040", "4802768", "7038832", "10315944", "15118786" ]
[ "nonn", "easy" ]
65
0
3
[ "A003274", "A069241", "A092526", "A174700", "A263719", "A302118" ]
[ "M1583" ]
N. J. A. Sloane
2024-11-27T12:41:33
oeisdata/seq/A003/A003274.seq
bf0ea9022009ed072361ff7684619d33
A003275
Values of phi(k) when phi(k) = phi(k+1).
[ "1", "2", "8", "48", "80", "96", "128", "240", "288", "480", "1008", "1200", "1296", "1440", "1728", "2592", "2592", "4800", "5600", "6480", "8640", "11040", "12480", "14976", "19008", "19200", "22464", "24320", "24576", "21120", "28416", "27840", "25920", "32000", "32768", "36000", "47520", "52992", "60480", "59904", "79200", "89280", "96768" ]
[ "nonn", "nice" ]
65
1
2
[ "A000010", "A001274", "A003275" ]
[ "M1874" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003275.seq
d4a9ca96ca023fcb3aef810ebd820c46
A003276
Numbers k such that the multiplicative group of residues prime to k, M_k, is isomorphic to M_{k+1}.
[ "1", "3", "15", "104", "495", "975", "22935", "32864", "57584", "131144", "491535", "2539004", "3988424", "6235215", "7378371", "13258575", "17949434", "25637744", "26879684", "29357475", "32235735", "41246864", "48615735", "184611375", "229944855", "257278724", "290849624", "429461864", "550666515", "671054835", "706075095" ]
[ "nonn", "nice" ]
36
1
2
[ "A001274", "A003276" ]
[ "M3000" ]
N. J. A. Sloane
2023-11-29T17:03:27
oeisdata/seq/A003/A003276.seq
cb0e2414408bcf9f4741b00a103ba810
A003277
Cyclic numbers: k such that k and phi(k) are relatively prime; also k such that there is just one group of order k, i.e., A000001(k) = 1.
[ "1", "2", "3", "5", "7", "11", "13", "15", "17", "19", "23", "29", "31", "33", "35", "37", "41", "43", "47", "51", "53", "59", "61", "65", "67", "69", "71", "73", "77", "79", "83", "85", "87", "89", "91", "95", "97", "101", "103", "107", "109", "113", "115", "119", "123", "127", "131", "133", "137", "139", "141", "143", "145", "149", "151", "157", "159", "161", "163", "167", "173" ]
[ "nonn", "nice", "easy" ]
171
1
2
[ "A000001", "A000010", "A002997", "A003277", "A005117", "A006094", "A008966", "A009195", "A036537", "A050384", "A051532", "A051953", "A054395", "A054396", "A054397", "A055561", "A056867", "A135850", "A249550", "A249551", "A249552", "A249553", "A249554", "A249555", "A253595" ]
[ "M0650" ]
N. J. A. Sloane and Richard Stanley
2025-01-25T23:00:37
oeisdata/seq/A003/A003277.seq
72a09de04f3db7b522b4a48bb7580491
A003278
Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), k.
[ "1", "2", "4", "5", "10", "11", "13", "14", "28", "29", "31", "32", "37", "38", "40", "41", "82", "83", "85", "86", "91", "92", "94", "95", "109", "110", "112", "113", "118", "119", "121", "122", "244", "245", "247", "248", "253", "254", "256", "257", "271", "272", "274", "275", "280", "281", "283", "284", "325", "326", "328", "329", "334", "335", "337", "338", "352", "353" ]
[ "nonn", "nice", "easy" ]
153
1
2
[ "A001511", "A003002", "A003278", "A005836", "A005837", "A005838", "A005839", "A020654", "A020655", "A020656", "A020657", "A020658", "A020659", "A020660", "A020661", "A020662", "A020663", "A020664", "A093682", "A098871", "A191106", "A229037", "A309890" ]
[ "M0975" ]
N. J. A. Sloane and Richard Stanley
2025-02-16T08:32:27
oeisdata/seq/A003/A003278.seq
6bda6bc223e6ac9c9189640136abba19
A003279
High temperature series for spherical model susceptibility on 3-dimensional simple cubic lattice.
[ "1", "6", "30", "144", "666", "3024", "13476", "59328", "258354", "1115856", "4784508", "20393856", "86473548", "365034816", "1534827960", "6431000832", "26862228450" ]
[ "nonn", "more" ]
22
0
2
null
[ "M4199" ]
N. J. A. Sloane
2023-10-22T01:25:53
oeisdata/seq/A003/A003279.seq
1599dc4cc84f02eb702f8e2ffb8ad3a5
A003280
Numerators of coefficients of Green function for cubic lattice.
[ "1", "9", "175", "2025", "102235", "1356047", "37160123", "6771931925", "772428184055", "189690563847015", "105217453376898775", "1548913291275244825", "2112565685454158552975", "1658173107161491979625" ]
[ "nonn", "easy", "frac" ]
17
0
2
null
[ "M4664" ]
N. J. A. Sloane
2023-10-21T23:45:57
oeisdata/seq/A003/A003280.seq
86d4a80408827b77b8de50b59ceca65e
A003281
Numerators of coefficients of Green function for cubic lattice.
[ "0", "1", "23", "1477", "555273", "38466649", "1711814393", "48275151899", "28127429172349", "11820256380127", "61330815490787739", "1438084556561535649", "3452174145433606905", "1300912433743549667989", "275638998008835888305243" ]
[ "nonn", "easy", "frac" ]
18
0
3
null
[ "M5137" ]
N. J. A. Sloane
2023-10-21T18:00:02
oeisdata/seq/A003/A003281.seq
abc25f9dfb41fb8a50b9c5994afbbc1a
A003282
Numerators of coefficients of Green function for cubic lattice.
[ "1", "1", "7", "19", "25", "67", "205", "3389", "24469", "151805", "3378595", "7529", "239951407", "10532699", "37801901", "553870985", "4729453873", "54466083977", "1974303293437", "73525821439", "36638106109621", "262239579597193", "2947415049407", "90871116596785" ]
[ "nonn", "easy", "frac" ]
22
0
3
[ "A003282", "A003283" ]
[ "M4360" ]
N. J. A. Sloane
2023-10-22T02:25:58
oeisdata/seq/A003/A003282.seq
d24fe9a6e35263328eebd18e9192c6d8
A003283
Denominators of coefficients of Green function for cubic lattice.
[ "1", "2", "20", "70", "112", "352", "1232", "22880", "183040", "1244672", "30098432", "72352", "2472371200", "115763200", "441223168", "6838959104", "61568122880", "745298329600", "28321336524800", "1103041527808", "573581594460160", "4275790067793920", "49961677422592" ]
[ "nonn", "easy", "frac" ]
23
0
2
[ "A003282", "A003283" ]
[ "M2116" ]
N. J. A. Sloane
2023-10-22T02:25:45
oeisdata/seq/A003/A003283.seq
38d8b58c422a076aa774deb74d562fca
A003284
Numerators of coefficients of Green function for cubic lattice.
[ "1", "1", "11", "19", "7861", "301259", "451526509", "6427914623", "16794274237", "12896029408223", "395798985324353", "30839190064680907", "164178854787337441961", "104746805369703910637", "30345665255129739404489" ]
[ "nonn", "easy", "frac" ]
19
0
3
[ "A003284", "A003298" ]
[ "M4777" ]
N. J. A. Sloane
2017-08-07T03:19:05
oeisdata/seq/A003/A003284.seq
7fb81bf5cd82a8e7d17f7e89dc4d1338
A003285
Period of continued fraction for square root of n (or 0 if n is a square).
[ "0", "1", "2", "0", "1", "2", "4", "2", "0", "1", "2", "2", "5", "4", "2", "0", "1", "2", "6", "2", "6", "6", "4", "2", "0", "1", "2", "4", "5", "2", "8", "4", "4", "4", "2", "0", "1", "2", "2", "2", "3", "2", "10", "8", "6", "12", "4", "2", "0", "1", "2", "6", "5", "6", "4", "2", "6", "7", "6", "4", "11", "4", "2", "0", "1", "2", "10", "2", "8", "6", "8", "2", "7", "5", "4", "12", "6", "4", "4", "2", "0", "1", "2", "2", "5", "10", "2", "6", "5", "2", "8", "8", "10", "16", "4", "4", "11", "4", "2", "0", "1", "2", "12" ]
[ "nonn", "nice" ]
131
1
3
[ "A003285", "A013943", "A035015", "A054269", "A061490", "A065938", "A067280", "A097853" ]
[ "M0018" ]
N. J. A. Sloane
2024-12-16T01:50:20
oeisdata/seq/A003/A003285.seq
b1a2e6199957377f8a4d031b391233ea
A003286
Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 2.
[ "1", "7", "66", "916", "16816", "373630", "9727010", "289374391", "9677492899", "359305262944", "14663732271505", "652463078546373", "31435363120551013", "1630394318463367718", "90570555840053284171", "5365261686125108336540", "337616338011820295406352", "22490263897737210321234701", "1581153614004788257326876764" ]
[ "nonn", "nice" ]
31
2
2
[ "A003286", "A129524", "A259471" ]
[ "M4441" ]
N. J. A. Sloane
2022-07-20T07:25:10
oeisdata/seq/A003/A003286.seq
e341a0043d714759bc07924c42d1ae17
A003287
Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).
[ "1", "4", "22", "140", "970", "7196", "56092", "452064", "3735700", "31484244", "269613896", "2339571468", "20529434520", "181871459580", "1624587752400", "14617165101216" ]
[ "nonn", "walk", "more" ]
36
1
2
[ "A001337", "A003287", "A003288", "A005398", "A005543", "A005544", "A005545", "A005546", "A005547", "A005548" ]
[ "M3588" ]
N. J. A. Sloane
2020-01-20T07:54:45
oeisdata/seq/A003/A003287.seq
7803c206cfd5c81d5b29a6b291c9be31
A003288
Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,0,2).
[ "4", "24", "152", "1080", "8152", "63976", "518232", "4299728", "36360872", "312284536", "2716694880", "23891215320", "212064567160", "1897551819416" ]
[ "nonn", "walk", "more" ]
30
2
1
[ "A003287", "A003288", "A005543", "A005544", "A005545", "A005546", "A005547", "A005548" ]
[ "M3600" ]
N. J. A. Sloane
2023-10-21T23:51:41
oeisdata/seq/A003/A003288.seq
c3ec139528b2bc77bced2c734e46a858
A003289
Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,1).
[ "1", "2", "4", "10", "30", "98", "328", "1140", "4040", "14542", "53060", "195624", "727790", "2728450", "10296720", "39084190", "149115456", "571504686", "2199310460", "8494701152", "32919635606", "127961125094", "498775164568", "1949112527750", "7634623480172" ]
[ "nonn", "walk", "more" ]
35
1
2
[ "A001335", "A003289", "A003290", "A003291", "A005549", "A005550", "A005551", "A005552", "A005553" ]
[ "M1229" ]
N. J. A. Sloane
2019-01-16T12:09:12
oeisdata/seq/A003/A003289.seq
dffcc6f624da7a278d91e312a27c25b4
A003290
Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,2).
[ "1", "6", "18", "50", "156", "508", "1724", "6018", "21440", "77632", "284706", "1055162", "3944956", "14858934", "56325420", "214698578", "822373244", "3163606784", "12217121138", "47343356398", "184038696776", "717456797490", "2804219712064", "10986639618642" ]
[ "nonn", "walk", "more" ]
28
2
2
[ "A001335", "A003289", "A003290", "A003291", "A005549", "A005550", "A005551", "A005552", "A005553" ]
[ "M4119" ]
N. J. A. Sloane
2021-12-26T20:42:10
oeisdata/seq/A003/A003290.seq
ee6916095e5896c1b1c91dc9993dc62c
A003291
Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,1).
[ "2", "6", "16", "46", "140", "464", "1580", "5538", "19804", "71884", "264204", "980778", "3671652", "13843808", "52519836", "200320878", "767688176", "2954410484", "11412815256", "44237340702", "171997272012", "670612394118", "2621415708492", "10271274034254" ]
[ "nonn", "walk", "more" ]
27
2
1
[ "A001335", "A003289", "A003290", "A003291", "A005549", "A005550", "A005551", "A005552", "A005553" ]
[ "M1613" ]
N. J. A. Sloane
2021-12-26T20:42:19
oeisdata/seq/A003/A003291.seq
25f748281b7995cc93576a2638c95231
A003292
Number of 4-line partitions of n decreasing across rows.
[ "1", "2", "4", "7", "11", "19", "29", "46", "70", "106", "156", "232", "334", "482", "686", "971", "1357", "1894", "2612", "3592", "4900", "6656", "8980", "12077", "16137", "21490", "28476", "37600", "49422", "64763", "84511", "109953", "142539", "184244", "237368", "304996", "390688", "499189", "636059", "808489", "1025017", "1296595", "1636173", "2060246", "2588440", "3245381", "4060519", "5070574" ]
[ "nonn", "easy" ]
36
1
2
null
[ "M1050" ]
N. J. A. Sloane
2017-10-13T12:18:00
oeisdata/seq/A003/A003292.seq
4b5094033e3fc247d9813b662a5ab01a
A003293
Number of planar partitions of n decreasing across rows.
[ "1", "1", "2", "4", "7", "12", "21", "34", "56", "90", "143", "223", "348", "532", "811", "1224", "1834", "2725", "4031", "5914", "8638", "12540", "18116", "26035", "37262", "53070", "75292", "106377", "149738", "209980", "293473", "408734", "567484", "785409", "1083817", "1491247", "2046233", "2800125", "3821959", "5203515" ]
[ "nonn", "easy", "nice" ]
107
0
3
[ "A000085", "A000219", "A003293", "A005308", "A005986", "A053529", "A138178", "A323432", "A323436" ]
[ "M1058" ]
N. J. A. Sloane
2023-10-29T01:44:05
oeisdata/seq/A003/A003293.seq
321b53499c4b5bf774d418fd4c8cfa81
A003294
Numbers k such that k^4 can be written as a sum of four positive 4th powers.
[ "353", "651", "706", "1059", "1302", "1412", "1765", "1953", "2118", "2471", "2487", "2501", "2604", "2824", "2829", "3177", "3255", "3530", "3723", "3883", "3906", "3973", "4236", "4267", "4333", "4449", "4557", "4589", "4942", "4949", "4974", "5002", "5208", "5281", "5295", "5463", "5491", "5543", "5648", "5658" ]
[ "nonn", "nice" ]
51
1
1
[ "A003294", "A039664", "A096739", "A138760" ]
[ "M5446" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003294.seq
f538f37facb866f694783ca18f8c0ef7
A003295
McKay-Thompson series of class 11A for the Monster group with a(0) = -5.
[ "1", "-5", "17", "46", "116", "252", "533", "1034", "1961", "3540", "6253", "10654", "17897", "29284", "47265", "74868", "117158", "180608", "275562", "415300", "620210", "916860", "1344251", "1953974", "2819664", "4038300", "5746031", "8122072", "11413112", "15943576", "22153909", "30620666" ]
[ "sign", "nice", "easy" ]
59
-1
2
[ "A000521", "A003295", "A007240", "A007241", "A007267", "A014708", "A045478", "A058205", "A128525", "A128663", "A134784" ]
[ "M3872" ]
N. J. A. Sloane
2018-05-12T18:50:28
oeisdata/seq/A003/A003295.seq
420c9b3abd0d912692f2691f1fd54e4a
A003296
Coefficients of modular function g_2(tau).
[ "1", "5", "19", "63", "185", "502", "1270", "3046", "6968", "15335", "32593", "67241", "135030", "264784", "508063", "955990", "1766742", "3211871", "5750824", "10153083", "17691868", "30454468", "51827503", "87259758", "145439278", "240113437", "392863105", "637330514", "1025589482" ]
[ "nonn", "nice" ]
24
1
2
null
[ "M3885" ]
N. J. A. Sloane
2022-01-31T01:22:31
oeisdata/seq/A003/A003296.seq
7427c31855348e596dd2171fe17e3b0e
A003297
Coefficients of modular function g_3(tau).
[ "1", "9", "49", "214", "800", "2685", "8274", "23829", "64843", "168223", "418723", "1005269", "2337340", "5281304", "11629334", "25015300", "52670865", "108745666", "220489361", "439619133", "862952442", "1669440245", "3185892198", "6002458625", "11173532683", "20564107275" ]
[ "nonn", "nice" ]
24
2
2
[ "A003296", "A003297" ]
[ "M4630" ]
N. J. A. Sloane
2022-01-31T01:22:23
oeisdata/seq/A003/A003297.seq
34d866804eefa82bc6b979bdc1f58b1c
A003298
Denominators of coefficients of Green function for cubic lattice.
[ "1", "18", "648", "2160", "1399680", "75582720", "149653785600", "2693768140800", "8620058050560", "7913213290414080", "284875678454906880", "25638811060941619200", "155678860762037511782400", "112088779748667008483328" ]
[ "nonn", "easy", "frac" ]
16
0
2
[ "A003284", "A003298" ]
[ "M5063" ]
N. J. A. Sloane
2017-08-06T22:46:03
oeisdata/seq/A003/A003298.seq
26061e4c55c429304ef910d6f8fc0606
A003299
Numerators of coefficients of Green function for cubic lattice.
[ "0", "1", "7", "5", "3635", "557485", "7596391", "19681954039", "32139541115", "11613832153165", "3386240626860905", "2153823021586357", "11330361348611303", "9397464146366084237", "9528720716522267278849", "309116925259099828695359" ]
[ "nonn", "easy", "frac" ]
16
0
3
[ "A003299", "A003300" ]
[ "M4331" ]
N. J. A. Sloane
2017-08-06T22:46:29
oeisdata/seq/A003/A003299.seq
514c318fba26704d06dbe7416dc45522
A003300
Denominators of coefficients of Green function for cubic lattice.
[ "1", "1", "18", "24", "27216", "5878656", "105815808", "346652587008", "693305174016", "299507835174912", "102431679629819904", "75255927891296256", "451535567347777536", "422637291037519773696", "479270688036547423371264" ]
[ "nonn", "easy", "frac" ]
16
0
3
[ "A003299", "A003300" ]
[ "M5053" ]
N. J. A. Sloane
2017-08-06T22:46:54
oeisdata/seq/A003/A003300.seq
5185dfd7a5c57c5c1b91d950dbee19e2