Datasets:
christopher
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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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A003401
Numbers of edges of regular polygons constructible with ruler (or, more precisely, an unmarked straightedge) and compass.
[ "1", "2", "3", "4", "5", "6", "8", "10", "12", "15", "16", "17", "20", "24", "30", "32", "34", "40", "48", "51", "60", "64", "68", "80", "85", "96", "102", "120", "128", "136", "160", "170", "192", "204", "240", "255", "256", "257", "272", "320", "340", "384", "408", "480", "510", "512", "514", "544", "640", "680", "768", "771", "816", "960", "1020", "1024", "1028", "1088", "1280", "1285" ]
[ "nonn", "nice" ]
189
1
2
[ "A000079", "A000215", "A002193", "A002194", "A003401", "A004169", "A004729", "A019434", "A046528", "A051916", "A092506", "A094214", "A099884", "A101263", "A101464", "A182007", "A228787", "A272534", "A272535", "A272536", "A293516", "A295298", "A295660", "A336469", "A336477" ]
[ "M0505" ]
N. J. A. Sloane, R. K. Guy
2025-02-16T08:32:27
oeisdata/seq/A003/A003401.seq
ca5febd21c97f21d4b4ebaf3ce2344b1
A003402
G.f.: 1/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)*(1-x^5)).
[ "1", "1", "2", "4", "6", "9", "14", "19", "27", "37", "49", "64", "84", "106", "134", "168", "207", "253", "309", "371", "445", "530", "626", "736", "863", "1003", "1163", "1343", "1543", "1766", "2017", "2291", "2597", "2935", "3305", "3712", "4161", "4647", "5181", "5763", "6394", "7079", "7825", "8627", "9497", "10436", "11445", "12531", "13702", "14952" ]
[ "nonn", "easy" ]
42
0
3
[ "A003402", "A003403", "A003404", "A003405", "A029073", "A256975", "A256976", "A256977", "A266755", "A266768", "A266769", "A266770", "A266775" ]
[ "M1003" ]
N. J. A. Sloane
2022-10-21T22:07:31
oeisdata/seq/A003/A003402.seq
4518f4bf8c4845b8b3e965253a75037e
A003403
G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i).
[ "1", "1", "2", "4", "7", "11", "18", "27", "41", "60", "87", "122", "172", "235", "320", "430", "572", "751", "982", "1268", "1629", "2074", "2625", "3297", "4123", "5118", "6324", "7771", "9506", "11567", "14023", "16917", "20335", "24343", "29039", "34510", "40885", "48265", "56811", "66661", "78001", "91001", "105901", "122902", "142291", "164329", "189347" ]
[ "nonn" ]
34
0
3
[ "A003402", "A003403", "A003404", "A003405", "A029073", "A256975", "A256976", "A256977" ]
[ "M1049" ]
N. J. A. Sloane
2024-01-31T10:48:00
oeisdata/seq/A003/A003403.seq
1de5442dee4fedbd538dcc3d655bbde4
A003404
Number of solid partitions of n supported on graph of cube.
[ "1", "1", "4", "7", "14", "23", "41", "63", "104", "152", "230", "327", "470", "647", "897", "1202", "1616", "2117", "2775", "3566", "4580", "5787", "7301", "9092", "11298", "13885", "17028", "20688", "25076", "30154", "36172", "43094", "51221", "60511", "71323", "83622", "97822", "113893", "132323", "153083" ]
[ "nonn", "nice", "easy" ]
31
0
3
[ "A003402", "A003403", "A003404", "A003405", "A029073", "A256975", "A256976", "A256977" ]
[ "M3310" ]
N. J. A. Sloane
2022-06-11T13:52:05
oeisdata/seq/A003/A003404.seq
8ab1c4c62c5008bc637daae8cc8d66a9
A003405
G.f.: (1 + x^4 + x^7 + 2*x^8 + x^9 + x^12 + x^16)/Product_{i=1..8} (1 - x^i).
[ "1", "1", "2", "3", "6", "8", "13", "19", "30", "41", "59", "80", "113", "149", "202", "264", "350", "447", "578", "730", "928", "1155", "1444", "1777", "2193", "2667", "3249", "3915", "4721", "5635", "6728", "7967", "9432", "11083", "13016", "15191", "17717", "20544", "23801", "27440", "31604", "36234", "41501", "47345", "53954", "61260", "69480", "78546", "88699" ]
[ "nonn" ]
35
0
3
[ "A003402", "A003403", "A003404", "A003405", "A029073", "A256975", "A256976", "A256977" ]
[ "M0754" ]
N. J. A. Sloane
2024-01-31T10:39:23
oeisdata/seq/A003/A003405.seq
856f10189195883911aee84e744f3310
A003406
Expansion of Ramanujan's function R(x) = 1 + Sum_{n >= 1} { x^(n*(n+1)/2) / ((1+x)(1+x^2)(1+x^3)...(1+x^n)) }.
[ "1", "1", "-1", "2", "-2", "1", "0", "1", "-2", "0", "2", "0", "-1", "-2", "2", "1", "0", "-2", "2", "-2", "0", "0", "3", "0", "-2", "-2", "1", "0", "2", "0", "0", "0", "-2", "0", "0", "1", "0", "0", "0", "2", "-1", "0", "-2", "-2", "0", "4", "0", "2", "-2", "0", "-2", "-1", "2", "0", "-2", "2", "0", "1", "0", "0", "0", "0", "-2", "0", "0", "0", "0", "-2", "4", "2", "-1", "0", "0", "-2", "-2", "-2", "2", "1", "2", "0", "0", "0", "0", "-2", "2", "0", "0", "-2", "2", "-2", "-2", "0", "3", "0", "0", "2", "0", "0", "0", "-2", "1", "-2", "0", "-2", "0" ]
[ "sign", "easy", "nice" ]
59
0
4
[ "A003406", "A003475", "A005895", "A005896", "A158690" ]
[ "M0206" ]
N. J. A. Sloane
2020-06-29T09:50:43
oeisdata/seq/A003/A003406.seq
4c525986e418e9a72db2e6fb6cccf056
A003407
Number of permutations of [n] with no 3-term arithmetic progression.
[ "1", "1", "2", "4", "10", "20", "48", "104", "282", "496", "1066", "2460", "6128", "12840", "29380", "74904", "212728", "368016", "659296", "1371056", "2937136", "6637232", "15616616", "38431556", "96547832", "198410168", "419141312", "941812088", "2181990978", "5624657008", "14765405996", "41918682488", "121728075232" ]
[ "nonn", "nice" ]
156
0
3
[ "A002620", "A003407", "A011782", "A162982", "A292523", "A296529" ]
[ "M1201" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003407.seq
c02bf7d28e670c45acd083676f6018d2
A003408
a(n) = binomial(3n+6, n).
[ "1", "9", "66", "455", "3060", "20349", "134596", "888030", "5852925", "38567100", "254186856", "1676056044", "11058116888", "73006209045", "482320623240", "3188675231420", "21094923659355", "139646485582065", "925029565741050", "6131164307078475", "40661170824914640", "269807672771096460" ]
[ "nonn", "easy" ]
59
0
2
null
[ "M4643" ]
N. J. A. Sloane, Simon Plouffe
2024-03-02T13:44:21
oeisdata/seq/A003/A003408.seq
f45870c0ec76836e5eb17e341e584171
A003409
a(n) = 3*binomial(2n-1,n).
[ "3", "9", "30", "105", "378", "1386", "5148", "19305", "72930", "277134", "1058148", "4056234", "15600900", "60174900", "232676280", "901620585", "3500409330", "13612702950", "53017895700", "206769793230", "807386811660", "3156148445580", "12350146091400", "48371405524650", "189615909656628", "743877799422156" ]
[ "nonn" ]
34
1
1
[ "A001700", "A003409" ]
[ "M2814" ]
N. J. A. Sloane
2023-10-23T12:38:47
oeisdata/seq/A003/A003409.seq
57f467a269445788893c2c2ab4503d96
A003410
Expansion of (1+x)(1+x^2)/(1-x-x^3).
[ "1", "2", "3", "5", "7", "10", "15", "22", "32", "47", "69", "101", "148", "217", "318", "466", "683", "1001", "1467", "2150", "3151", "4618", "6768", "9919", "14537", "21305", "31224", "45761", "67066", "98290", "144051", "211117", "309407", "453458", "664575", "973982", "1427440", "2092015", "3065997", "4493437", "6585452", "9651449" ]
[ "nonn", "easy" ]
63
0
2
[ "A003410", "A038718", "A058278", "A097333", "A171855" ]
[ "M0648" ]
N. J. A. Sloane
2023-08-11T11:33:24
oeisdata/seq/A003/A003410.seq
7fa14d047cfd07c52a342ace5fbd6058
A003411
Losing initial positions in game: two players alternate in removing >= 1 stones; last player wins; first player may not remove all stones; each move <= 3 times previous move.
[ "1", "2", "3", "4", "6", "8", "11", "15", "21", "29", "40", "55", "76", "105", "145", "200", "276", "381", "526", "726", "1002", "1383", "1909", "2635", "3637", "5020", "6929", "9564", "13201", "18221", "25150", "34714", "47915", "66136", "91286", "126000", "173915", "240051", "331337", "457337", "631252", "871303", "1202640", "1659977" ]
[ "nonn", "easy" ]
41
0
2
[ "A003411", "A048590" ]
[ "M0561" ]
N. J. A. Sloane, R. K. Guy, Rodney W. Topor (rwt(AT)cit.gu.edu.au)
2022-04-13T13:25:16
oeisdata/seq/A003/A003411.seq
04d5ce6b37779e5d4884a43124117611
A003412
From a nim-like game.
[ "1", "2", "3", "4", "6", "8", "11", "14", "18", "24", "32", "43", "54", "68", "86", "110", "142", "185", "239", "307", "393", "503", "645", "830", "1069", "1376", "1769", "2272", "2917", "3747", "4816", "6192", "7961", "10233", "13150", "16897", "21713", "27905", "35866", "46099", "59249", "76146", "97859", "125764", "161630", "207729", "266978" ]
[ "nonn" ]
26
0
2
[ "A003412", "A005708" ]
[ "M0559" ]
N. J. A. Sloane
2017-06-22T07:00:58
oeisdata/seq/A003/A003412.seq
57800fe38fafa4cfa14e0326350d1987
A003413
From a nim-like game.
[ "1", "2", "3", "4", "5", "7", "9", "12", "15", "19", "24", "31", "40", "52", "67", "86", "110", "141", "181", "233", "300", "386", "496", "637", "818", "1051", "1351", "1737", "2233", "2870", "3688", "4739", "6090", "7827", "10060", "12930", "16618", "21357", "27447", "35274", "45334", "58264", "74882", "96239", "123686", "158960", "204294", "262558" ]
[ "nonn" ]
37
0
2
[ "A003413", "A005708" ]
[ "M0521" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A003/A003413.seq
8650c895fd51d929cafaef8003e18f95
A003414
a(n) = floor( Bernoulli(2*n)/(-4*n) ).
[ "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-2", "13", "-141", "1803", "-27414", "487468", "-10026348", "236192433", "-6317862398", "190439655626", "-6425425249653", "241207241774250", "-10020155328258127", "458387180159766538", "-22989944171828251746", "1259023596072554784854", "-75008667460769643668558" ]
[ "sign" ]
24
1
9
[ "A000367", "A002445", "A003414" ]
null
N. J. A. Sloane
2023-10-21T19:51:09
oeisdata/seq/A003/A003414.seq
735424b1b850841ddc767087fd430f13
A003415
a(n) = n' = arithmetic derivative of n: a(0) = a(1) = 0, a(prime) = 1, a(m*n) = m*a(n) + n*a(m).
[ "0", "0", "1", "1", "4", "1", "5", "1", "12", "6", "7", "1", "16", "1", "9", "8", "32", "1", "21", "1", "24", "10", "13", "1", "44", "10", "15", "27", "32", "1", "31", "1", "80", "14", "19", "12", "60", "1", "21", "16", "68", "1", "41", "1", "48", "39", "25", "1", "112", "14", "45", "20", "56", "1", "81", "16", "92", "22", "31", "1", "92", "1", "33", "51", "192", "18", "61", "1", "72", "26", "59", "1", "156", "1", "39", "55", "80", "18", "71" ]
[ "nonn", "easy", "nice", "hear", "look" ]
366
0
5
[ "A001787", "A002620", "A003415", "A003557", "A024451", "A027471", "A038554", "A051674", "A057521", "A068237", "A068238", "A068311", "A068312", "A068327", "A068328", "A068329", "A068346", "A068719", "A068720", "A068721", "A069359", "A083345", "A083347", "A083348", "A085708", "A085731", "A086131", "A086134", "A096371", "A098699", "A098700", "A099301", "A099302", "A099303", "A099304", "A099305", "A099306", "A099307", "A099308", "A099309", "A099310", "A129150", "A129151", "A129152", "A157037", "A165560", "A168386", "A185232", "A189481", "A190121", "A192192", "A229501", "A235991", "A235992", "A256750", "A258057", "A258644", "A258645", "A258646", "A258647", "A258648", "A258649", "A258650", "A258651", "A258851", "A260619", "A260620", "A263111", "A300251", "A302055", "A305809", "A319684", "A322582", "A327860", "A327863", "A327864", "A327865", "A327928", "A327929", "A327963", "A327965", "A327978", "A328099", "A328234", "A328235", "A328236", "A328239", "A328243", "A328244", "A328246", "A328248", "A328251", "A328252", "A328303", "A328310", "A328320", "A328321", "A328383", "A328393", "A328768", "A328769", "A328845", "A328846", "A341998", "A342001", "A342003", "A342014", "A342925", "A348507", "A349133", "A349173", "A349380", "A349394", "A349618", "A349619", "A349620", "A349621", "A349905", "A369049", "A369251", "A369252" ]
[ "M3196" ]
N. J. A. Sloane, R. K. Guy
2024-07-20T08:17:56
oeisdata/seq/A003/A003415.seq
e7385c07e7bc76445827ae26041c4ea5
A003416
Sociable numbers: smallest member of each cycle (conjectured).
[ "12496", "14316", "1264460", "2115324", "2784580", "4938136", "7169104", "18048976", "18656380", "28158165", "46722700", "81128632", "174277820", "209524210", "330003580", "498215416", "805984760", "1095447416", "1236402232", "1276254780", "1799281330" ]
[ "nonn" ]
66
1
1
[ "A003416", "A052470", "A072890", "A072891", "A122726" ]
null
N. J. A. Sloane
2025-03-12T10:38:00
oeisdata/seq/A003/A003416.seq
4c215d7052d5ca881c620572d38caf3e
A003417
Continued fraction for e.
[ "2", "1", "2", "1", "1", "4", "1", "1", "6", "1", "1", "8", "1", "1", "10", "1", "1", "12", "1", "1", "14", "1", "1", "16", "1", "1", "18", "1", "1", "20", "1", "1", "22", "1", "1", "24", "1", "1", "26", "1", "1", "28", "1", "1", "30", "1", "1", "32", "1", "1", "34", "1", "1", "36", "1", "1", "38", "1", "1", "40", "1", "1", "42", "1", "1", "44", "1", "1", "46", "1", "1", "48", "1", "1", "50", "1", "1", "52", "1", "1", "54", "1", "1", "56", "1", "1", "58", "1", "1", "60", "1", "1", "62", "1", "1", "64", "1", "1", "66" ]
[ "nonn", "cofr", "nice", "easy", "changed" ]
183
0
1
[ "A001113", "A001204", "A003417", "A005131", "A006083", "A006084", "A006085", "A007676", "A007677", "A058282", "A081750", "A342991" ]
[ "M0088" ]
N. J. A. Sloane
2025-04-15T13:04:32
oeisdata/seq/A003/A003417.seq
41711521411f0c60fb116e98f9698f49
A003418
Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1.
[ "1", "1", "2", "6", "12", "60", "60", "420", "840", "2520", "2520", "27720", "27720", "360360", "360360", "360360", "720720", "12252240", "12252240", "232792560", "232792560", "232792560", "232792560", "5354228880", "5354228880", "26771144400", "26771144400", "80313433200", "80313433200", "2329089562800", "2329089562800" ]
[ "nonn", "easy", "core", "nice" ]
473
0
3
[ "A000142", "A000793", "A002110", "A002182", "A002201", "A002944", "A003418", "A014963", "A020500", "A025527", "A025528", "A038610", "A051173", "A064446", "A064859", "A069513", "A072938", "A093880", "A094348", "A096179", "A099996", "A102910", "A106037", "A119682", "A133233", "A179661", "A193181", "A225558", "A225630", "A225632", "A225640", "A225642", "A275120", "A276781" ]
[ "M1590" ]
Roland Anderson (roland.anderson(AT)swipnet.se)
2025-04-12T11:18:10
oeisdata/seq/A003/A003418.seq
ddae01e76ceeed2e9f4664dff950d4b3
A003419
Values of m in the discriminant D = 4*m leading to a new minimum of the L-function of the Dirichlet series L(1) = Sum_{k>0} Kronecker(D,k)/k.
[ "1", "2", "17", "167", "227", "362", "398", "331427", "430022", "737183", "800663", "821498", "1475858", "2271407", "3009173", "5417453" ]
[ "nonn", "more" ]
30
1
2
[ "A003419", "A003420", "A003421", "A003521" ]
[ "M2102" ]
N. J. A. Sloane
2020-02-07T12:09:07
oeisdata/seq/A003/A003419.seq
1f5912fff399dd5d55007f6a959ed9aa
A003420
Values of m in the discriminant D = -4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k=1..oo} Kronecker(D,k)/k.
[ "1", "2", "5", "11", "14", "26", "41", "89", "101", "194", "314", "341", "689", "1091", "1154", "1889", "2141", "3449", "3506", "5561", "6254", "8126", "8774", "10709", "13166", "15461", "23201", "24569", "30014", "81149", "81626", "162686", "243374", "644474", "839354", "879941" ]
[ "nonn", "more" ]
35
1
2
[ "A003420", "A003521", "A331949" ]
[ "M1387" ]
N. J. A. Sloane
2022-08-27T21:31:23
oeisdata/seq/A003/A003420.seq
8f08820a2bd956f3a352465b9227ef07
A003421
Nonsquare values of m in the discriminant D = 4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k>0} Kronecker(D,k)/k.
[ "2", "3", "6", "7", "10", "19", "31", "34", "46", "79", "106", "151", "211", "214", "274", "331", "394", "631", "751", "919", "991", "1054", "1486", "1654", "2146", "2479", "2599", "3826", "5014", "5251", "7459", "8551", "9454", "10651", "13666", "18379", "22234", "32971", "39274", "45046", "48799", "61051", "62386", "74299", "78439", "84319", "111094" ]
[ "nonn" ]
22
1
1
[ "A003419", "A003420", "A003421", "A003521" ]
[ "M0750" ]
N. J. A. Sloane
2020-02-07T12:08:47
oeisdata/seq/A003/A003421.seq
e1db89b5b19b8b069a30d6e1a7d15faa
A003422
Left factorials: !n = Sum_{k=0..n-1} k!.
[ "0", "1", "2", "4", "10", "34", "154", "874", "5914", "46234", "409114", "4037914", "43954714", "522956314", "6749977114", "93928268314", "1401602636314", "22324392524314", "378011820620314", "6780385526348314", "128425485935180314", "2561327494111820314", "53652269665821260314", "1177652997443428940314" ]
[ "nonn", "easy", "nice" ]
280
0
3
[ "A000045", "A000108", "A000110", "A000142", "A000166", "A000178", "A000204", "A003422", "A005165", "A007489", "A008276", "A014144", "A014288", "A049782", "A094216", "A094638", "A100612", "A101752", "A102411", "A102412", "A102639", "A135722", "A137338", "A227157", "A232845", "A357145" ]
[ "M1237" ]
N. J. A. Sloane, R. K. Guy
2025-02-16T08:32:27
oeisdata/seq/A003/A003422.seq
85200b58a7a61584249b3866442b56fe
A003423
a(n) = a(n-1)^2 - 2, with a(0) = 6.
[ "6", "34", "1154", "1331714", "1773462177794", "3145168096065837266706434", "9892082352510403757550172975146702122837936996354" ]
[ "nonn", "easy" ]
96
0
1
[ "A001566", "A003010", "A003423", "A003487", "A145505" ]
[ "M4215" ]
N. J. A. Sloane
2025-01-12T13:37:15
oeisdata/seq/A003/A003423.seq
ada99f6de5a707ce71e3af018956b8d9
A003424
Primes of form (p^x - 1)/(p^y - 1), p prime.
[ "3", "5", "7", "13", "17", "31", "73", "127", "257", "307", "757", "1093", "1723", "2801", "3541", "5113", "8011", "8191", "10303", "17293", "19531", "28057", "30103", "30941", "65537", "86143", "88741", "131071", "147073" ]
[ "nonn", "easy" ]
26
1
1
[ "A003424", "A059055", "A085104" ]
[ "M2417" ]
N. J. A. Sloane
2023-10-21T18:29:52
oeisdata/seq/A003/A003424.seq
48337681ec985302a969dbf63037f4f3
A003425
n! times number of posets with n elements.
[ "1", "1", "6", "114", "5256", "507720", "93616560", "30894489360", "17407086641280", "16152167106391680", "23990233574783750400", "55735096448700749203200", "198720975339675515386598400", "1070118060127292955589511500800", "8585695098723146508385537345689600", "101432601341702692223559539854263552000" ]
[ "nonn" ]
19
0
3
[ "A000142", "A001035", "A003425" ]
[ "M4294" ]
N. J. A. Sloane
2022-05-22T16:21:07
oeisdata/seq/A003/A003425.seq
11306b0f7a6718d97b3f847da41ff322
A003426
Number of stable trees with n nodes.
[ "1", "1", "1", "1", "2", "4", "8", "17", "37", "85", "196", "469", "1134", "2799", "6975", "17628", "44903", "115497", "299089", "780036", "2045924", "5396078", "14299878", "38067356", "101748748", "272995157", "735004112", "1985356350", "5378958683", "14614641597", "39813346977", "108730631236", "297641593852" ]
[ "nonn" ]
30
1
5
[ "A003426", "A006544" ]
[ "M1142" ]
N. J. A. Sloane
2023-10-21T19:59:30
oeisdata/seq/A003/A003426.seq
5d0bd40673bb21aa98f3cd92952f8ef6
A003427
Number of trees by stability index.
[ "0", "0", "0", "0", "1", "1", "1", "2", "4", "8", "16", "34", "72", "158", "348", "784", "1777", "4080", "9425", "21965", "51456", "121300", "287215", "683268", "1631532", "3910235", "9401000", "22670058", "54813780", "132867903" ]
[ "nonn", "more" ]
18
1
8
null
[ "M1134" ]
N. J. A. Sloane
2023-10-21T18:32:11
oeisdata/seq/A003/A003427.seq
04fdd743e37e97ac317c4d0983ffa74a
A003428
Number of trees by stability index.
[ "0", "0", "0", "0", "0", "0", "2", "3", "5", "12", "22", "47", "94", "201", "417", "907", "1948", "4289", "9440", "21063", "47124", "106377", "240980", "549272", "1256609", "2888057", "6660347", "15416623", "35794121", "83362301" ]
[ "nonn", "more" ]
17
1
7
null
[ "M0738" ]
N. J. A. Sloane
2023-10-21T18:32:47
oeisdata/seq/A003/A003428.seq
c1dfda0c318dbaa8ff19c2e5f24b09d9
A003429
Number of trees with stability index n.
[ "5", "7", "15", "27", "57", "114", "243", "506", "1102", "2381", "5269", "11686", "26277", "59348", "135317", "310064", "715475", "1659321", "3870414", "9071915", "21372782", "50591199", "120332237" ]
[ "nonn", "more" ]
17
1
1
null
[ "M3765" ]
N. J. A. Sloane
2023-10-21T18:33:15
oeisdata/seq/A003/A003429.seq
1bf05428c0c8a41972a341dfac080fc9
A003430
Number of unlabeled series-parallel posets (i.e., generated by unions and sums) with n nodes.
[ "1", "1", "2", "5", "15", "48", "167", "602", "2256", "8660", "33958", "135292", "546422", "2231462", "9199869", "38237213", "160047496", "674034147", "2854137769", "12144094756", "51895919734", "222634125803", "958474338539", "4139623680861", "17931324678301", "77880642231286", "339093495674090", "1479789701661116" ]
[ "easy", "nonn", "nice" ]
77
0
3
[ "A000084", "A003430", "A003431", "A007453", "A007454", "A048172", "A339156", "A339159", "A339225", "A339228", "A339231" ]
[ "M1476" ]
N. J. A. Sloane, Richard Stanley, and Mira Bernstein
2020-12-02T13:57:16
oeisdata/seq/A003/A003430.seq
52ece30bd93814f98ad79ef878ea4580
A003431
Number of isomorphism classes of connected irreducible posets with n labeled points.
[ "1", "1", "0", "0", "1", "12", "104", "956", "10037", "126578", "1971005", "38569954", "958347642", "30400603560", "1234260982770", "64187360439352", "4275470549123119" ]
[ "nonn", "nice", "more" ]
39
0
6
[ "A003430", "A003431", "A046906" ]
[ "M4857" ]
N. J. A. Sloane and Richard Stanley
2022-07-10T14:58:33
oeisdata/seq/A003/A003431.seq
09c5cc7d2a3a4b08463f09d8685f2da5
A003432
Hadamard maximal determinant problem: largest determinant of a (real) {0,1}-matrix of order n.
[ "1", "1", "1", "2", "3", "5", "9", "32", "56", "144", "320", "1458", "3645", "9477", "25515", "131072", "327680", "1114112", "3411968", "19531250", "56640625", "195312500" ]
[ "nonn", "hard", "more", "nice" ]
106
0
4
[ "A003432", "A003433", "A013588", "A036297", "A051752" ]
[ "M0720" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003432.seq
d58bb87a859ddbcdabd704524341d42b
A003433
Hadamard maximal determinant problem: largest determinant of (+1,-1)-matrix of order n.
[ "1", "2", "4", "16", "48", "160", "576", "4096", "14336", "73728", "327680", "2985984", "14929920", "77635584", "418037760", "4294967296", "21474836480", "146028888064", "894426939392", "10240000000000", "59392000000000", "409600000000000" ]
[ "nonn", "hard", "nice" ]
75
1
2
[ "A003432", "A003433", "A051753", "A188895" ]
[ "M1291" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003433.seq
9ba725fb5401caecfd438c3d6e15951e
A003434
Number of iterations of phi(x) at n needed to reach 1.
[ "0", "1", "2", "2", "3", "2", "3", "3", "3", "3", "4", "3", "4", "3", "4", "4", "5", "3", "4", "4", "4", "4", "5", "4", "5", "4", "4", "4", "5", "4", "5", "5", "5", "5", "5", "4", "5", "4", "5", "5", "6", "4", "5", "5", "5", "5", "6", "5", "5", "5", "6", "5", "6", "4", "6", "5", "5", "5", "6", "5", "6", "5", "5", "6", "6", "5", "6", "6", "6", "5", "6", "5", "6", "5", "6", "5", "6", "5", "6", "6", "5", "6", "7", "5", "7", "5", "6", "6", "7", "5", "6", "6", "6", "6", "6", "6", "7", "5", "6", "6", "7", "6", "7", "6", "6" ]
[ "nonn", "easy", "nice", "look" ]
82
1
3
[ "A000010", "A003434", "A007755" ]
[ "M0244" ]
N. J. A. Sloane
2022-02-28T12:19:51
oeisdata/seq/A003/A003434.seq
aa17e9662f309723ec7209c342e49ec4
A003435
Number of directed Hamiltonian circuits on n-octahedron with a marked starting node.
[ "8", "192", "11904", "1125120", "153262080", "28507207680", "6951513784320", "2153151603671040", "826060810479206400", "384600188992919961600", "213656089636192754073600", "139620366072628402087526400", "106033731334825319789808844800" ]
[ "nonn", "nice", "easy" ]
56
2
1
[ "A003435", "A003436", "A003437", "A129348" ]
[ "M4578" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003435.seq
876f970fc3c8f47d75d8d4cd9c9db1b8
A003436
Number of inequivalent labeled Hamiltonian circuits on n-octahedron. Interlacing chords joining 2n points on circle.
[ "1", "0", "1", "4", "31", "293", "3326", "44189", "673471", "11588884", "222304897", "4704612119", "108897613826", "2737023412199", "74236203425281", "2161288643251828", "67228358271588991", "2225173863019549229", "78087247031912850686", "2896042595237791161749", "113184512236563589997407" ]
[ "nonn", "easy", "nice" ]
107
0
4
[ "A000179", "A000296", "A000699", "A000806", "A001147", "A003435", "A003436", "A003437", "A005493", "A129348", "A170941", "A190823", "A278990", "A306386", "A306419", "A322402", "A324011", "A324172", "A324173", "A324428" ]
[ "M3638" ]
N. J. A. Sloane
2024-08-01T10:54:17
oeisdata/seq/A003/A003436.seq
4a4423f65179cbd11324ff0270b085db
A003437
Number of unlabeled Hamiltonian circuits on n-octahedron (cross polytope); also number of circular chord diagrams with n chords, modulo symmetries.
[ "0", "1", "2", "7", "29", "196", "1788", "21994", "326115", "5578431", "107026037", "2269254616", "52638064494", "1325663757897", "36021577975918", "1050443713185782", "32723148860301935", "1084545122297249077", "38105823782987999742", "1414806404051118314077" ]
[ "nonn", "nice" ]
54
1
3
[ "A003436", "A003437", "A007474", "A278990" ]
[ "M1781" ]
N. J. A. Sloane
2020-07-28T11:17:46
oeisdata/seq/A003/A003437.seq
e42516955ac1bc5044ff793639445719
A003438
Number of 5 X 5 matrices with nonnegative integer entries and row and column sums equal to n.
[ "1", "120", "6210", "153040", "2224955", "22069251", "164176640", "976395820", "4855258305", "20856798285", "79315936751", "272095118010", "854560160105", "2486299719645", "6765755480415", "17356306529251", "42250330784180", "98137852369965" ]
[ "nonn", "easy", "nice" ]
34
0
2
[ "A001496", "A002817", "A003438", "A005466", "A019298", "A058391", "A257493" ]
[ "M5381" ]
N. J. A. Sloane
2023-06-25T20:05:57
oeisdata/seq/A003/A003438.seq
12a1b362644b6bedd07cbab412295199
A003439
Number of 6 X 6 stochastic matrices of integers: all rows and columns sum to n.
[ "1", "720", "202410", "20933840", "1047649905", "30767936616", "602351808741", "8575979362560", "94459713879600", "842286559093240", "6292583664553881", "40447642842118656", "228438173705550566", "1152877640765297760", "5271278793334883190", "22085628572718605376", "85604721304213863531" ]
[ "nonn" ]
30
0
2
[ "A003439", "A005467", "A257493" ]
[ "M5474" ]
N. J. A. Sloane
2020-04-09T22:26:11
oeisdata/seq/A003/A003439.seq
368dd5a4519ffc127749790d986a91d7
A003440
Number of binary vectors with restricted repetitions.
[ "1", "1", "3", "7", "17", "42", "104", "259", "648", "1627", "4098", "10350", "26202", "66471", "168939", "430071", "1096451", "2799072", "7154189", "18305485", "46885179", "120195301", "308393558", "791882862", "2034836222", "5232250537", "13462265079", "34657740889", "89272680921", "230069128392" ]
[ "nonn" ]
50
0
3
[ "A003440", "A078678", "A104402", "A177790" ]
[ "M2666" ]
N. J. A. Sloane
2023-07-06T01:55:37
oeisdata/seq/A003/A003440.seq
8af8e530fdbc0dc1546f584c05814d25
A003441
Number of nonequivalent dissections of a polygon into n triangles by nonintersecting diagonals rooted at a cell up to rotation.
[ "1", "1", "3", "10", "30", "99", "335", "1144", "3978", "14000", "49742", "178296", "643856", "2340135", "8554275", "31429068", "115997970", "429874830", "1598952498", "5967382200", "22338765540", "83859016956", "315614844558", "1190680751376", "4501802224520", "17055399281284" ]
[ "nonn" ]
39
1
3
[ "A003441", "A295222" ]
[ "M2840" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003441.seq
b410db054076e11753b1e16563a818b9
A003442
Number of nonequivalent dissections of an n-gon into (n-3) polygons by nonintersecting diagonals rooted at a cell up to rotation.
[ "1", "2", "11", "48", "208", "858", "3507", "14144", "56698", "226100", "898942", "3565920", "14124496", "55887930", "220985795", "873396480", "3450940830", "13633173180", "53855628554", "212750148000", "840496068160", "3320817060132", "13122294166126", "51860761615488" ]
[ "nonn" ]
39
4
2
[ "A003442", "A003443", "A003454", "A220881", "A295622" ]
[ "M2002" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003442.seq
f3039e2f2a6365b4da9e11a3081bb747
A003443
Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation.
[ "1", "3", "24", "150", "825", "4205", "20384", "95472", "436050", "1954150", "8629528", "37665030", "162845865", "698599125", "2977488000", "12620579140", "53243068230", "223707978090", "936619554000", "3909283969500", "16272003594658", "67565854800378", "279942274434624" ]
[ "nonn" ]
34
5
2
[ "A003442", "A003443", "A003454" ]
[ "M3104" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003443.seq
0036965c23c5657cc2c95d2c94ac9836
A003444
Number of dissections of a polygon.
[ "1", "4", "12", "43", "143", "504", "1768", "6310", "22610", "81752", "297160", "1086601", "3991995", "14732720", "54587280", "202997670", "757398510", "2834510744", "10637507400", "40023636310", "150946230006", "570534578704", "2160865067312", "8199711378716", "31170212479588", "118686578956272" ]
[ "nonn" ]
34
4
2
[ "A003444", "A003445", "A003450", "A047996", "A073020", "A220881" ]
[ "M3455" ]
N. J. A. Sloane
2023-11-29T06:58:37
oeisdata/seq/A003/A003444.seq
160be807a2db76bd0dcd45ab18f87923
A003445
Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals up to rotation.
[ "1", "2", "8", "40", "165", "712", "2912", "11976", "48450", "195580", "784504", "3139396", "12526605", "49902440", "198499200", "788795924", "3131945190", "12428258796", "49295766000", "195464345440", "774857314042", "3071175790232", "12171403236288", "48233597481200", "191138095393700", "757436171945952" ]
[ "nonn" ]
34
5
2
[ "A003443", "A003444", "A003445", "A003448", "A003450", "A220881", "A295633" ]
[ "M1859" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003445.seq
6f6f3d5010f06f1f4e55607463c24299
A003446
Number of nonequivalent dissections of a polygon into n triangles by nonintersecting diagonals rooted at a cell up to rotation and reflection.
[ "0", "1", "1", "2", "6", "16", "52", "170", "579", "1996", "7021", "24892", "89214", "321994", "1170282", "4277352", "15715249", "57999700", "214939846", "799478680", "2983699498", "11169391168", "41929537871", "157807451672", "595340479694", "2250901216266", "8527700012092", "32369067177176" ]
[ "nonn", "easy", "nice" ]
46
0
4
[ "A003446", "A295259" ]
[ "M1616" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003446.seq
127886a78b3aff64fad8340243e3a50d
A003447
Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.
[ "1", "2", "7", "26", "108", "434", "1765", "7086", "28384", "113092", "449582", "1783092", "7062611", "27944394", "110494113", "436699670", "1725474562", "6816591452", "26927828642", "106375090796", "420248084468", "1660408588852", "6561147261682", "25930381015756", "102496390643352", "405212762977544" ]
[ "nonn" ]
29
4
2
[ "A003447", "A003448", "A003452", "A003456" ]
[ "M1772" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003447.seq
2376081ebe7ff0905eded25edf12a636
A003448
Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.
[ "1", "3", "15", "81", "422", "2124", "10223", "47813", "218130", "977354", "4315130", "18833538", "81424236", "349303352", "1488748719", "6310303727", "26621551418", "111854042306", "468309841090", "1954642186302", "8136002036672", "33782928166668", "139971138117190", "578803145957026" ]
[ "nonn" ]
22
5
2
[ "A003447", "A003448" ]
[ "M2993" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003448.seq
97ece870d5e387b0ed302c7f606387fa
A003449
Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals up to rotation and reflection.
[ "1", "1", "3", "7", "24", "74", "259", "891", "3176", "11326", "40942", "148646", "543515", "1996212", "7367075", "27294355", "101501266", "378701686", "1417263770", "5318762098", "20011847548", "75473144396", "285267393358", "1080432637662", "4099856060808", "15585106611244", "59343290815356" ]
[ "nonn" ]
42
4
3
[ "A003449", "A003450", "A295419", "A295634" ]
[ "M2687" ]
N. J. A. Sloane
2023-11-29T06:58:41
oeisdata/seq/A003/A003449.seq
79788ab006cfe058dcb5f2898f13d547
A003450
Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals up to rotation and reflection.
[ "1", "2", "6", "24", "89", "371", "1478", "6044", "24302", "98000", "392528", "1570490", "6264309", "24954223", "99253318", "394409402", "1565986466", "6214173156", "24647935156", "97732340680", "387428854374", "1535588541762", "6085702368796", "24116801236744", "95569050564444", "378718095630676" ]
[ "nonn" ]
37
5
2
[ "A003444", "A003445", "A003449", "A003450", "A220881", "A295419", "A295634" ]
[ "M1673" ]
N. J. A. Sloane
2023-11-29T06:58:48
oeisdata/seq/A003/A003450.seq
724d6a0c98ccb749ac4ac6f5c47ea457
A003451
Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals up to rotation.
[ "1", "4", "8", "16", "25", "40", "56", "80", "105", "140", "176", "224", "273", "336", "400", "480", "561", "660", "760", "880", "1001", "1144", "1288", "1456", "1625", "1820", "2016", "2240", "2465", "2720", "2976", "3264", "3553", "3876", "4200", "4560", "4921", "5320", "5720", "6160", "6601", "7084", "7568", "8096", "8625", "9200", "9776", "10400" ]
[ "nonn" ]
54
5
2
[ "A003451", "A003453", "A006584", "A027656", "A295633" ]
[ "M3330" ]
N. J. A. Sloane
2023-06-25T20:07:41
oeisdata/seq/A003/A003451.seq
1a0bbdfc568dd219277cd34a4a41e705
A003452
Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.
[ "2", "7", "15", "28", "45", "69", "98", "136", "180", "235", "297", "372", "455", "553", "660", "784", "918", "1071", "1235", "1420", "1617", "1837", "2070", "2328", "2600", "2899", "3213", "3556", "3915", "4305", "4712", "5152", "5610", "6103", "6615", "7164", "7733", "8341", "8970", "9640", "10332", "11067", "11825", "12628" ]
[ "nonn" ]
21
5
1
[ "A003447", "A003452" ]
[ "M1742" ]
N. J. A. Sloane
2021-01-19T11:48:00
oeisdata/seq/A003/A003452.seq
21ff1af896566043aa10dcc3703a730d
A003453
Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals up to rotation and reflection.
[ "1", "3", "6", "11", "17", "26", "36", "50", "65", "85", "106", "133", "161", "196", "232", "276", "321", "375", "430", "495", "561", "638", "716", "806", "897", "1001", "1106", "1225", "1345", "1480", "1616", "1768", "1921", "2091", "2262", "2451", "2641", "2850", "3060", "3290", "3521", "3773", "4026" ]
[ "nonn", "easy", "nice" ]
74
5
2
[ "A003453", "A005744", "A213847", "A295419", "A295634" ]
[ "M2542" ]
N. J. A. Sloane, Simon Plouffe
2021-01-19T11:48:00
oeisdata/seq/A003/A003453.seq
ef1a9d7d5eacd302faf7cee5d5357aed
A003454
Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation.
[ "1", "2", "6", "25", "107", "509", "2468", "12258", "61797", "315830", "1630770", "8498303", "44629855", "235974495", "1255105304", "6710883952", "36050676617", "194478962422", "1053120661726", "5722375202661", "31191334491891", "170504130213135", "934495666529380", "5134182220623958", "28270742653671621" ]
[ "nonn" ]
37
3
2
[ "A001004", "A003442", "A003454", "A003455", "A003456", "A005033", "A295222" ]
[ "M1676" ]
N. J. A. Sloane
2022-03-22T02:26:08
oeisdata/seq/A003/A003454.seq
393bb0c70f30174dcc5355744a5c8c48
A003455
Number of nonequivalent dissections of an n-gon by nonintersecting diagonals up to rotation.
[ "1", "2", "3", "11", "29", "122", "479", "2113", "9369", "43392", "203595", "975563", "4736005", "23296394", "115811855", "581324861", "2942579633", "15008044522", "77064865555", "398150807179", "2068470765261", "10800665952376", "56658467018647", "298489772155137", "1578702640556193" ]
[ "nonn" ]
22
3
2
[ "A001004", "A003454", "A003455", "A003456", "A005034", "A295224", "A295495" ]
[ "M0909" ]
N. J. A. Sloane
2021-12-26T14:25:17
oeisdata/seq/A003/A003455.seq
1c8fca7ecc999239e1994f93201d5e3b
A003456
Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation and reflection.
[ "1", "2", "5", "17", "62", "275", "1272", "6225", "31075", "158376", "816229", "4251412", "22319056", "117998524", "627573216", "3355499036", "18025442261", "97239773408", "526560862829", "2861189112867", "15595669996482", "85252072993968", "467247847612316", "2567091151780343" ]
[ "nonn" ]
23
3
2
[ "A001004", "A003454", "A003455", "A003456", "A005035", "A295259" ]
[ "M1509" ]
N. J. A. Sloane
2021-12-26T14:25:29
oeisdata/seq/A003/A003456.seq
f737fbaa1b3e97c6486ae214a6cd9bcf
A003457
a(n) = ceiling(Bernoulli(2n)/(-4n)).
[ "0", "1", "0", "1", "0", "1", "0", "1", "-1", "14", "-140", "1804", "-27413", "487469", "-10026347", "236192434", "-6317862397", "190439655627", "-6425425249652", "241207241774251", "-10020155328258126", "458387180159766539", "-22989944171828251745", "1259023596072554784855", "-75008667460769643668557" ]
[ "sign" ]
20
1
10
[ "A003414", "A003457" ]
null
N. J. A. Sloane
2017-06-22T05:37:34
oeisdata/seq/A003/A003457.seq
25de775d3547a902187be3ac48147b47
A003458
Erdős-Selfridge function: a(n) is the least number m > n+1 such that the least prime factor of binomial(m, n) is > n.
[ "3", "6", "7", "7", "23", "62", "143", "44", "159", "46", "47", "174", "2239", "239", "719", "241", "5849", "2098", "2099", "43196", "14871", "19574", "35423", "193049", "2105", "36287", "1119", "284", "240479", "58782", "341087", "371942", "6459", "69614", "37619", "152188", "152189", "487343", "767919", "85741", "3017321" ]
[ "easy", "nonn", "nice" ]
45
1
1
null
[ "M2515" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:27
oeisdata/seq/A003/A003458.seq
6bfc127de38b853e0039617f41884b12
A003459
Absolute primes (or permutable primes): every permutation of the digits is a prime.
[ "2", "3", "5", "7", "11", "13", "17", "31", "37", "71", "73", "79", "97", "113", "131", "199", "311", "337", "373", "733", "919", "991", "1111111111111111111", "11111111111111111111111" ]
[ "nonn", "base", "nice", "hard" ]
116
1
1
[ "A002275", "A003459", "A004022", "A004023", "A010051", "A016114", "A023107", "A039986", "A103443", "A129338", "A141263", "A258706" ]
[ "M0658" ]
N. J. A. Sloane
2024-09-22T18:29:43
oeisdata/seq/A003/A003459.seq
3bb0f68008c46da9f0a59d749d85108b
A003460
Octal formula for dragon curve of order n.
[ "1", "6", "154", "66344", "15471166144", "663447306235471066144", "1547116614473162154311663447306215471066144" ]
[ "nonn" ]
27
1
2
null
[ "M4300" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003460.seq
dfda3d14161760eb972ae5113bc75d89
A003461
Bode numbers multiplied by 10: 4 + 3*floor(2^(n-1)).
[ "4", "7", "10", "16", "28", "52", "100", "196", "388", "772", "1540", "3076", "6148", "12292", "24580", "49156", "98308", "196612", "393220", "786436", "1572868", "3145732", "6291460", "12582916", "25165828", "50331652", "100663300", "201326596", "402653188", "805306372", "1610612740", "3221225476" ]
[ "nonn", "easy", "nice" ]
72
0
1
[ "A003461", "A061654", "A087009" ]
[ "M3302" ]
N. J. A. Sloane, based on correspondence from W. I. McLaughlin, 1974.
2021-06-25T06:20:21
oeisdata/seq/A003/A003461.seq
36691a30ce2cf68e91f460f6ef45f721
A003462
a(n) = (3^n - 1)/2.
[ "0", "1", "4", "13", "40", "121", "364", "1093", "3280", "9841", "29524", "88573", "265720", "797161", "2391484", "7174453", "21523360", "64570081", "193710244", "581130733", "1743392200", "5230176601", "15690529804", "47071589413", "141214768240", "423644304721", "1270932914164" ]
[ "nonn", "easy", "nice" ]
409
0
3
[ "A000225", "A000392", "A003462", "A004125", "A006516", "A014753", "A028491", "A033622", "A036562", "A036564", "A036569", "A039755", "A055875", "A059443", "A064099", "A065363", "A097933", "A113047", "A120444", "A179526", "A321872", "A341590", "A367967", "A367968" ]
[ "M3463" ]
N. J. A. Sloane
2025-03-14T15:05:04
oeisdata/seq/A003/A003462.seq
092d11b8d5f7b8d8d161a59e39485057
A003463
a(n) = (5^n - 1)/4.
[ "0", "1", "6", "31", "156", "781", "3906", "19531", "97656", "488281", "2441406", "12207031", "61035156", "305175781", "1525878906", "7629394531", "38146972656", "190734863281", "953674316406", "4768371582031", "23841857910156", "119209289550781", "596046447753906", "2980232238769531" ]
[ "nonn", "easy" ]
181
0
3
[ "A002275", "A002450", "A002452", "A003462", "A003463", "A003464", "A004061", "A023000", "A023001", "A026375", "A045468", "A060458", "A074479", "A086122", "A107219" ]
[ "M4209" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003463.seq
35dec09b00f171ef5390d1d7cc5fb025
A003464
a(n) = (6^n - 1)/5.
[ "0", "1", "7", "43", "259", "1555", "9331", "55987", "335923", "2015539", "12093235", "72559411", "435356467", "2612138803", "15672832819", "94036996915", "564221981491", "3385331888947", "20311991333683", "121871948002099", "731231688012595", "4387390128075571" ]
[ "nonn", "easy" ]
110
0
3
null
[ "M4425" ]
N. J. A. Sloane
2025-03-14T15:05:13
oeisdata/seq/A003/A003464.seq
f7992ee1c389e70cddb8b1e1128fec7e
A003465
Number of ways to cover an n-set.
[ "1", "1", "5", "109", "32297", "2147321017", "9223372023970362989", "170141183460469231667123699502996689125", "57896044618658097711785492504343953925273862865136528166133547991141168899281" ]
[ "nonn", "easy", "nice" ]
93
0
3
[ "A000110", "A000371", "A003465", "A007537", "A055154", "A055621", "A186021", "A326914", "A326962", "A369950" ]
[ "M4024" ]
N. J. A. Sloane
2025-03-09T12:27:30
oeisdata/seq/A003/A003465.seq
b2a118fe6cc676e6b855d120a71221fe
A003466
Number of minimal covers of an n-set that have exactly one point which appears in more than one set in the cover.
[ "0", "3", "28", "210", "1506", "10871", "80592", "618939", "4942070", "41076508", "355372524", "3198027157", "29905143464", "290243182755", "2920041395248", "30414515081650", "327567816748638", "3643600859114439", "41809197852127240", "494367554679088923", "6017481714095327410" ]
[ "nonn" ]
32
2
2
[ "A003466", "A046165", "A282575" ]
[ "M3117" ]
N. J. A. Sloane
2023-10-21T19:51:53
oeisdata/seq/A003/A003466.seq
4a5766e32390da48a0b4f2d0781199a3
A003467
Number of minimal covers of an n-set that cover exactly 3 points uniquely.
[ "5", "28", "190", "1340", "9065", "57512", "344316", "1966440", "10813935", "57672340", "299893594", "1526727748", "7633634645", "37580965520", "182536112120", "876173330832", "4161823312731", "19585050873180", "91396904062870", "423311976698380", "1947235092796609", "8901646138480568" ]
[ "nonn", "easy" ]
39
3
1
[ "A003467", "A035347" ]
[ "M3951" ]
N. J. A. Sloane
2023-10-21T18:39:13
oeisdata/seq/A003/A003467.seq
ce17a9375f8ff553014d428d72fefcd4
A003468
Number of minimal 3-covers of a labeled n-set.
[ "1", "22", "305", "3410", "33621", "305382", "2619625", "21554170", "171870941", "1337764142", "10216988145", "76862115330", "571247591461", "4203844925302", "30687029023865", "222518183370890", "1604626924403181", "11518132293452862" ]
[ "nonn" ]
67
3
2
[ "A000302", "A000392", "A003468", "A005060", "A005783", "A005786", "A016103", "A016111", "A046166", "A046169", "A055066", "A057668", "A143496" ]
[ "M5125" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003468.seq
9054b26a3188196f6c57d44705fa63d6
A003469
Number of minimal covers of an (n + 1)-set by a collection of n nonempty subsets, a(n) = A035348(n,n-1).
[ "1", "6", "22", "65", "171", "420", "988", "2259", "5065", "11198", "24498", "53157", "114583", "245640", "524152", "1113959", "2359125", "4980546", "10485550", "22019865", "46137091", "96468716", "201326292", "419430075", "872414881", "1811938950", "3758095978", "7784627789", "16106126895", "33285996048" ]
[ "nonn", "easy" ]
71
1
2
[ "A003469", "A053218", "A053221" ]
[ "M4153" ]
N. J. A. Sloane
2023-11-22T06:32:45
oeisdata/seq/A003/A003469.seq
dcffc31d33961f018ab155b8204f11bb
A003470
a(n) = n*a(n-1) - a(n-2) + 1 + (-1)^n.
[ "1", "1", "3", "8", "31", "147", "853", "5824", "45741", "405845", "4012711", "43733976", "520795003", "6726601063", "93651619881", "1398047697152", "22275111534553", "377278848390249", "6768744159489931", "128228860181918440", "2557808459478878871", "53585748788874537851", "1176328664895760953853" ]
[ "nonn", "easy" ]
63
0
3
[ "A003470", "A008279", "A072374", "A086764", "A143409" ]
[ "M2759" ]
N. J. A. Sloane and John Riordan
2022-11-25T10:41:22
oeisdata/seq/A003/A003470.seq
2858b5708151bb22dc90e1972efa4eed
A003471
Number of permutations with no hits on 2 main diagonals.
[ "1", "0", "0", "0", "4", "16", "80", "672", "4752", "48768", "440192", "5377280", "59245120", "839996160", "10930514688", "176547098112", "2649865335040", "48047352500224", "817154768973824", "16438490531536896", "312426715251262464", "6906073926286725120", "145060238642780180480", "3495192502897779875840" ]
[ "nonn", "easy", "nice" ]
82
0
5
[ "A000166", "A002777", "A003471", "A225740", "A335872" ]
[ "M3525" ]
N. J. A. Sloane
2024-12-29T14:08:02
oeisdata/seq/A003/A003471.seq
f33611cfb58d612b6012cb54b58357df
A003472
a(n) = 2^(n-4)*C(n,4).
[ "1", "10", "60", "280", "1120", "4032", "13440", "42240", "126720", "366080", "1025024", "2795520", "7454720", "19496960", "50135040", "127008768", "317521920", "784465920", "1917583360", "4642570240", "11142168576", "26528972800", "62704844800", "147220070400" ]
[ "nonn", "easy", "nice" ]
83
4
2
[ "A001787", "A001788", "A001789", "A003472", "A038207" ]
[ "M4718" ]
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A003/A003472.seq
491dbcc1b17c58c85d36b61ea3980878
A003473
Generalized Euler phi function (for p=2).
[ "1", "2", "3", "8", "15", "24", "49", "128", "189", "480", "1023", "1536", "4095", "6272", "10125", "32768", "65025", "96768", "262143", "491520", "583443", "2095104", "4190209", "6291456", "15728625", "33546240", "49545027", "102760448", "268435455", "331776000", "887503681", "2147483648", "3211797501", "8522956800", "12325233375", "25367150592", "68719476735", "137438429184", "206007472125" ]
[ "nonn" ]
59
1
2
[ "A003473", "A003474", "A027362", "A086479", "A192037" ]
[ "M0875" ]
N. J. A. Sloane
2025-02-19T01:04:35
oeisdata/seq/A003/A003473.seq
c5aa407980d05df67027391a0977acbb
A003474
Generalized Euler phi function (for p=3).
[ "1", "4", "18", "32", "160", "324", "1456", "2048", "13122", "25600", "117128", "209952", "913952", "2119936", "9447840", "13107200", "86093440", "172186884", "774840976", "1310720000", "6964002864", "13718968384", "62761410632", "88159684608", "557885504000", "835308258304", "5083731656658", "8988257288192", "45753584909920", "89261680665600", "411782264189296", "564050001920000" ]
[ "nonn" ]
37
1
2
[ "A003473", "A003474", "A192037" ]
[ "M3541" ]
N. J. A. Sloane
2025-02-19T01:07:12
oeisdata/seq/A003/A003474.seq
c09ac4c947752cf8e50a4cda89526a00
A003475
Expansion of Sum_{k>0} (-1)^(k+1) q^(k^2) / ((1-q)(1-q^3)(1-q^5)...(1-q^(2k-1))).
[ "1", "1", "1", "0", "0", "0", "-1", "-1", "0", "-1", "-1", "0", "-1", "0", "1", "-1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "-1", "0", "0", "0", "1", "-1", "-1", "-1", "0", "0", "-1", "0", "-1", "0", "0", "-1", "-1", "-1", "1", "0", "-1", "0", "0", "0", "1", "0", "-1", "0", "0", "1", "0", "1", "1", "0", "1", "-1", "1", "0", "0", "2", "0", "0", "0", "1", "0", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "1", "-1", "-1", "1", "0", "0", "0", "-1", "-2", "0", "0", "-1", "0", "1", "0", "-1", "-1", "-1", "0", "0", "0" ]
[ "sign" ]
45
1
70
[ "A003406", "A003475", "A053251", "A158690" ]
null
N. J. A. Sloane
2020-08-06T00:31:06
oeisdata/seq/A003/A003475.seq
e2742b3441372739c0d35162209c7047
A003476
a(n) = a(n-1) + 2*a(n-3).
[ "1", "2", "3", "5", "9", "15", "25", "43", "73", "123", "209", "355", "601", "1019", "1729", "2931", "4969", "8427", "14289", "24227", "41081", "69659", "118113", "200275", "339593", "575819", "976369", "1655555", "2807193", "4759931", "8071041", "13685427", "23205289", "39347371", "66718225", "113128803", "191823545", "325259995" ]
[ "nonn", "easy" ]
44
1
2
[ "A003229", "A003476", "A052537", "A078044" ]
[ "M0705" ]
N. J. A. Sloane
2023-10-21T19:24:06
oeisdata/seq/A003/A003476.seq
f2387e358f88d6865c72c50564163529
A003477
Expansion of 1/((1-2x)(1+x^2)(1-x-2x^3)).
[ "1", "3", "6", "14", "33", "71", "150", "318", "665", "1375", "2830", "5798", "11825", "24039", "48742", "98606", "199113", "401455", "808382", "1626038", "3267809", "6562295", "13169814", "26416318", "52962681", "106145855", "212665582", "425965126", "853005201", "1707833095", "3418756806" ]
[ "nonn", "easy" ]
82
0
2
[ "A003230", "A003477", "A077854", "A077949" ]
[ "M2579" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A003/A003477.seq
c7539f01952eb112fe4c8ff4b5aeaa88
A003478
Expansion of 1/((1-2*x)*(1-x-2*x^3)).
[ "1", "3", "7", "17", "39", "85", "183", "389", "815", "1693", "3495", "7173", "14655", "29837", "60567", "122645", "247855", "500061", "1007495", "2027493", "4076191", "8188333", "16437623", "32978613", "66132495", "132562173", "265628263", "532110981", "1065670783", "2133798221", "4271762007", "8550587221", "17113150959" ]
[ "nonn", "easy" ]
52
0
2
null
[ "M2662" ]
N. J. A. Sloane
2023-10-21T19:57:53
oeisdata/seq/A003/A003478.seq
643291d0409a6d0854212adb43e46834
A003479
Expansion of 1/((1-x)*(1-x-2*x^3)).
[ "1", "2", "3", "6", "11", "18", "31", "54", "91", "154", "263", "446", "755", "1282", "2175", "3686", "6251", "10602", "17975", "30478", "51683", "87634", "148591", "251958", "427227", "724410", "1228327", "2082782", "3531603", "5988258", "10153823", "17217030", "29193547", "49501194", "83935255", "142322350" ]
[ "easy", "nonn" ]
47
0
2
[ "A003229", "A003479" ]
[ "M0781" ]
N. J. A. Sloane
2023-10-21T23:48:46
oeisdata/seq/A003/A003479.seq
3b7672da3e5be9bdb522d893f971a20d
A003480
a(n) = 4*a(n-1) - 2*a(n-2) (n >= 3).
[ "1", "2", "7", "24", "82", "280", "956", "3264", "11144", "38048", "129904", "443520", "1514272", "5170048", "17651648", "60266496", "205762688", "702517760", "2398545664", "8189147136", "27959497216", "95459694592", "325919783936", "1112759746560", "3799199418368", "12971278180352", "44286713884672", "151204299177984" ]
[ "nonn", "easy", "nice" ]
202
0
2
[ "A000129", "A001003", "A001835", "A003480", "A006012", "A007052", "A007070", "A029744", "A059576", "A126764", "A145839", "A145840", "A145841", "A181289", "A228405", "A261780" ]
[ "M1763" ]
N. J. A. Sloane
2025-02-25T10:35:34
oeisdata/seq/A003/A003480.seq
f9791f355e51bad59bb359e537c0437f
A003481
a(n) = 7*a(n-1) - a(n-2) + 5.
[ "2", "20", "143", "986", "6764", "46367", "317810", "2178308", "14930351", "102334154", "701408732", "4807526975", "32951280098", "225851433716", "1548008755919", "10610209857722", "72723460248140", "498454011879263", "3416454622906706", "23416728348467684", "160500643816367087", "1100087778366101930" ]
[ "nonn", "easy" ]
46
0
1
[ "A003481", "A033888" ]
[ "M2120" ]
N. J. A. Sloane
2023-10-21T23:40:42
oeisdata/seq/A003/A003481.seq
2b01be5d6a21cd60956d8ccd55d3ad15
A003482
a(n) = 7*a(n-1) - a(n-2) + 4, with a(0) = 0, a(1) = 5.
[ "0", "5", "39", "272", "1869", "12815", "87840", "602069", "4126647", "28284464", "193864605", "1328767775", "9107509824", "62423800997", "427859097159", "2932589879120", "20100270056685", "137769300517679", "944284833567072", "6472224534451829", "44361286907595735", "304056783818718320" ]
[ "nonn", "easy" ]
83
0
2
[ "A000045", "A001109", "A001654", "A003482", "A081018", "A206351" ]
[ "M3988" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003482.seq
c7cce332c711cace1bf5f3a7930b2d15
A003483
Number of square permutations of n elements.
[ "1", "1", "1", "3", "12", "60", "270", "1890", "14280", "128520", "1096200", "12058200", "139043520", "1807565760", "22642139520", "339632092800", "5237183952000", "89032127184000", "1475427973219200", "28033131491164800", "543494606861606400", "11413386744093734400", "235075995738558374400", "5406747901986842611200", "126214560713084056012800" ]
[ "nonn", "easy", "nice" ]
97
0
4
[ "A003483", "A103619", "A103620", "A215716", "A215717", "A215718", "A246945", "A247005", "A247621" ]
[ "M2931" ]
N. J. A. Sloane
2024-07-14T08:42:55
oeisdata/seq/A003/A003483.seq
fce68dad037d976ee99a5dc860b1ed3d
A003484
Radon function, also called Hurwitz-Radon numbers.
[ "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "9", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "10", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "9", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "12", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "9", "1", "2", "1", "4", "1", "2", "1", "8", "1", "2", "1", "4", "1", "2", "1", "10", "1", "2", "1", "4", "1", "2" ]
[ "nonn", "easy", "core", "nice", "mult" ]
103
1
2
[ "A003484", "A003485", "A006519", "A007814", "A053381", "A101119" ]
[ "M0161" ]
N. J. A. Sloane
2022-10-22T08:05:41
oeisdata/seq/A003/A003484.seq
f24efee9ac1e3df2ca61300f6caa0f3d
A003485
Hurwitz-Radon function at powers of 2.
[ "1", "2", "4", "8", "9", "10", "12", "16", "17", "18", "20", "24", "25", "26", "28", "32", "33", "34", "36", "40", "41", "42", "44", "48", "49", "50", "52", "56", "57", "58", "60", "64", "65", "66", "68", "72", "73", "74", "76", "80", "81", "82", "84", "88", "89", "90", "92", "96", "97", "98", "100", "104", "105", "106", "108", "112", "113", "114", "116", "120", "121", "122", "124" ]
[ "easy", "nonn", "nice" ]
65
0
2
[ "A003484", "A003485", "A008621", "A047466", "A047507", "A209675" ]
[ "M1086" ]
N. J. A. Sloane
2023-12-15T19:16:57
oeisdata/seq/A003/A003485.seq
a95491f10efc5f53f52ebcb93c768a24
A003486
a(n) = (n^2 + 1)*3^n.
[ "1", "6", "45", "270", "1377", "6318", "26973", "109350", "426465", "1614006", "5963949", "21611934", "77058945", "271034910", "942244893", "3242852982", "11063007297", "37450647270", "125911658925", "420738651054", "1398200544801", "4623476115726" ]
[ "nonn", "easy" ]
26
0
2
null
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A003/A003486.seq
61d35c659ebbfb1416c99e3316fbbd4f
A003487
a(n) = a(n-1)^2 - 2, with a(0) = 5.
[ "5", "23", "527", "277727", "77132286527", "5949389624883225721727", "35395236908668169265765137996816180039862527", "1252822795820745419377249396736955608088527968701950139470082687906021780162741058825727" ]
[ "nonn", "easy" ]
64
0
1
[ "A001566", "A001601", "A003010", "A003423", "A003487", "A145504" ]
[ "M3926" ]
N. J. A. Sloane
2025-01-12T13:08:54
oeisdata/seq/A003/A003487.seq
8feac9c6c99a2879837068eb92f0a845
A003488
High temperature series for spin-1/2 Ising surface susceptibility on planar hexagonal lattice.
[ "4", "36", "232", "1308", "6808", "33560", "159108" ]
[ "nonn", "more" ]
18
1
1
null
[ "M3662" ]
N. J. A. Sloane
2023-10-21T23:48:21
oeisdata/seq/A003/A003488.seq
a0e950dec306d90a19778d34ec0816c6
A003489
High temperature series for spin-1/2 Ising surface susceptibility on square lattice.
[ "4", "20", "84", "292", "980", "3052", "9316", "27396", "79412" ]
[ "nonn", "more" ]
14
1
1
null
[ "M3564" ]
N. J. A. Sloane
2023-10-21T23:48:17
oeisdata/seq/A003/A003489.seq
2582d302cea184d50f4cf91ba3b58d2d
A003490
High temperature series for spin-1/2 Ising surface susceptibility on 3-dimensional simple cubic lattice.
[ "2", "20", "142", "880", "5106", "28252", "152142", "799736", "4141426", "21133476", "106827054" ]
[ "nonn", "more" ]
18
1
1
null
[ "M2119" ]
N. J. A. Sloane
2023-10-21T23:48:14
oeisdata/seq/A003/A003490.seq
07fbc29b5dcdc2ae5b4717cb471c5850
A003491
High temperature series for spin-1/2 Ising surface susceptibility on f.c.c. lattice.
[ "8", "152", "2200", "28520", "347416", "4068024", "46360392" ]
[ "nonn", "more" ]
16
1
1
null
[ "M4576" ]
N. J. A. Sloane
2023-10-21T23:48:10
oeisdata/seq/A003/A003491.seq
ef436a3036da6ca8604bab5297d3f721
A003492
High temperature series for spin-1/2 Ising surface susceptibility on b.c.c. lattice.
[ "8", "88", "840", "6888", "54824", "412712", "3065096", "22134152" ]
[ "nonn", "more" ]
16
1
1
null
[ "M4562" ]
N. J. A. Sloane
2023-10-21T23:48:07
oeisdata/seq/A003/A003492.seq
f3164c8449310ef6b761c1f97165cca6
A003493
High temperature series for spin-1/2 Ising surface susceptibility on square lattice.
[ "2", "12", "50", "180", "606", "1924", "5910", "17564", "51186", "146180" ]
[ "nonn", "more" ]
14
1
1
null
[ "M2022" ]
N. J. A. Sloane
2023-10-21T23:48:03
oeisdata/seq/A003/A003493.seq
2595b90385367a87b0bb83c8ef80550c
A003494
High temperature series for susceptibility for spherical model on b.c.c. lattice.
[ "1", "8", "56", "384", "2536", "16512", "105664", "669696", "4201832", "26183808", "162073408", "998129664", "6117389760", "37346353152", "227164816896", "1377490599936", "8328848160360" ]
[ "nonn", "more" ]
19
0
2
[ "A002914", "A003279", "A003494", "A003495", "A003497" ]
[ "M4543" ]
N. J. A. Sloane
2023-10-19T07:37:36
oeisdata/seq/A003/A003494.seq
4685db3d6ce26c3eb0673568567d5ee5
A003495
High temperature series for susceptibility for spherical model on f.c.c. lattice.
[ "1", "12", "132", "1392", "14292", "144000", "1430592", "14057280", "136914804", "1323843936", "12722294736", "121625850240", "1157512059936", "10972654675200", "103654156958208", "976153872234240", "9167420099612340" ]
[ "nonn", "more" ]
19
0
2
[ "A002921", "A003279", "A003494", "A003495", "A003498" ]
[ "M4865" ]
N. J. A. Sloane
2023-10-19T07:37:42
oeisdata/seq/A003/A003495.seq
390b13ef05d6170a2984d4a4ad4e95fa
A003496
High temperature series for spherical model internal energy on 3-dimensional simple cubic lattice.
[ "1", "6", "18", "132", "810", "5724", "42156", "323352", "2550042", "20559660", "168680196" ]
[ "nonn", "more" ]
18
0
2
null
[ "M4127" ]
N. J. A. Sloane
2023-10-21T23:47:59
oeisdata/seq/A003/A003496.seq
5fb8e74453c44e8966a4ccc0fe6ec27e
A003497
Internal energy series for b.c.c. lattice.
[ "1", "8", "88", "1216", "19160", "327232", "5896896", "110393856", "2126213592", "41861519680", "838733719616" ]
[ "nonn", "more" ]
16
0
2
null
[ "M4563" ]
N. J. A. Sloane
2023-10-21T23:47:56
oeisdata/seq/A003/A003497.seq
232c89c6e3715f3dd2df96b692a58594
A003498
High temperature series for internal energy for spherical model on f.c.c. lattice.
[ "1", "12", "48", "252", "1440", "8544", "52416", "330588", "2130240", "13961808", "92784384", "623772288", "4234688640", "28990262016", "199908428544", "1387276513308", "9681052037760", "67895140257840", "478281284627328", "3382695596455344" ]
[ "nonn", "more" ]
19
0
2
[ "A003495", "A003496", "A003497", "A003498", "A047712" ]
[ "M4839" ]
N. J. A. Sloane
2023-10-19T07:37:47
oeisdata/seq/A003/A003498.seq
aa9eeb7644b7fe809db1ab33f663a013
A003499
a(n) = 6*a(n-1) - a(n-2), with a(0) = 2, a(1) = 6.
[ "2", "6", "34", "198", "1154", "6726", "39202", "228486", "1331714", "7761798", "45239074", "263672646", "1536796802", "8957108166", "52205852194", "304278004998", "1773462177794", "10336495061766", "60245508192802", "351136554095046", "2046573816377474", "11928306344169798", "69523264248641314" ]
[ "nonn", "easy" ]
216
0
1
[ "A002203", "A003499", "A081555", "A103999", "A174501", "A188645" ]
[ "M1701" ]
N. J. A. Sloane
2023-04-20T13:18:54
oeisdata/seq/A003/A003499.seq
9cd3d862dd6d559c455264bf6f20aa66
A003500
a(n) = 4*a(n-1) - a(n-2) with a(0) = 2, a(1) = 4.
[ "2", "4", "14", "52", "194", "724", "2702", "10084", "37634", "140452", "524174", "1956244", "7300802", "27246964", "101687054", "379501252", "1416317954", "5285770564", "19726764302", "73621286644", "274758382274", "1025412242452", "3826890587534", "14282150107684", "53301709843202", "198924689265124" ]
[ "nonn", "easy", "nice" ]
250
0
1
[ "A001075", "A001353", "A001570", "A001835", "A002530", "A003500", "A005320", "A006051", "A011943", "A011945", "A016064", "A019673", "A048788", "A102344", "A105531", "A174500", "A268281", "A334277", "A335025" ]
[ "M1278" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003500.seq
431e0f05222bf2e5d614ccc4921ba9e5