Datasets:
christopher
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oeis

Dataset card Data Studio Files
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666,262,453B
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timestamp
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A005301
Representation degeneracies for Neveu-Schwarz strings.
[ "1", "1", "4", "4", "13", "19", "39", "59", "112", "169", "294", "448", "735", "1110", "1757" ]
[ "nonn" ]
8
1
3
null
[ "M3233" ]
N. J. A. Sloane.
2015-08-23T11:43:31
oeisdata/seq/A005/A005301.seq
c05dd610dfb6e09d3d49c0f2056a7d33
A005302
Representation degeneracies for Neveu-Schwarz strings.
[ "1", "1", "6", "7", "18", "29", "59", "92", "171", "267", "457", "709", "1155", "1763" ]
[ "nonn" ]
8
2
3
null
[ "M4061" ]
N. J. A. Sloane.
2015-08-23T11:43:55
oeisdata/seq/A005/A005302.seq
f58b4355347293b59ee2f319ec9f2da3
A005303
Representation degeneracies for Ramond strings.
[ "1", "0", "2", "4", "6", "12", "22", "36", "62", "104", "166", "268", "426", "660", "1022", "1564", "2358", "3540", "5266", "7756", "11362", "16524", "23854", "34252", "48890", "69368", "97942", "137588", "192314", "267628", "370798", "511524", "702886" ]
[ "nonn", "easy" ]
15
0
3
null
[ "M1024" ]
N. J. A. Sloane.
2015-01-14T13:29:23
oeisdata/seq/A005/A005303.seq
861a184f27c6320049fb701ba7c23164
A005304
Representation degeneracies for Ramond strings.
[ "2", "2", "4", "10", "18", "32", "58", "98", "164", "274", "442", "704", "1114", "1730", "2660", "4058", "6114", "9136", "13554", "19930" ]
[ "nonn", "more" ]
26
1
1
null
[ "M0336" ]
N. J. A. Sloane.
2017-09-13T10:54:04
oeisdata/seq/A005/A005304.seq
fd4fc15747cdf3e5caa6565823333c7e
A005305
Representation degeneracies for Ramond strings.
[ "2", "4", "8", "16", "30", "56", "100", "172", "290", "480", "780", "1248", "1970", "3068", "4724", "7200", "10862", "16240", "24080" ]
[ "nonn", "more" ]
12
2
1
null
[ "M1117" ]
N. J. A. Sloane
2015-01-17T19:43:18
oeisdata/seq/A005/A005305.seq
7b9015595c647b27047a9c292cd17b35
A005306
Representation degeneracies for Ramond strings.
[ "2", "4", "10", "22", "40", "76", "138", "238", "408", "682", "1112", "1792", "2844", "4444", "6872", "10510", "15896", "23834" ]
[ "nonn", "more" ]
17
3
1
null
[ "M1202" ]
N. J. A. Sloane
2015-01-15T03:55:42
oeisdata/seq/A005/A005306.seq
d875cf7f81b6100cc80dddf577877a41
A005307
Bosonic string states.
[ "1", "-1", "0", "0", "1", "0", "1", "0", "2", "0", "3", "1", "6", "2", "9", "6", "16" ]
[ "sign" ]
16
0
9
null
[ "M0028" ]
N. J. A. Sloane
2015-08-23T12:10:42
oeisdata/seq/A005/A005307.seq
8b8857a5e254cf0988cb977bc8aa3d8e
A005308
Bosonic string states.
[ "1", "0", "0", "0", "1", "1", "2", "2", "4", "4", "7", "8", "14", "16", "25", "31", "47", "58", "85", "107", "153", "195", "271", "348", "480", "616", "834", "1077", "1445", "1863", "2478", "3194", "4216", "5431", "7118", "9157", "11942", "15329", "19884", "25485", "32916", "42090", "54147", "69093", "88563", "112769", "144056", "183028", "233112", "295525" ]
[ "nonn" ]
46
1
7
[ "A003293", "A005308", "A005986" ]
[ "M0310" ]
N. J. A. Sloane
2024-12-28T10:19:53
oeisdata/seq/A005/A005308.seq
f7d4902cdd450b7ac32330b4586b4f31
A005309
Fermionic string states.
[ "1", "0", "2", "4", "8", "16", "32", "60", "114", "212", "384", "692", "1232", "2160", "3760", "6480", "11056", "18728", "31474", "52492", "86976", "143176", "234224", "380988", "616288", "991624", "1587600", "2529560", "4011808", "6334656", "9960080", "15596532", "24327122", "37801568", "58525152", "90291232", "138825416" ]
[ "nonn" ]
33
0
3
[ "A005309", "A156616", "A261386", "A261389", "A261451", "A261452" ]
[ "M1125" ]
N. J. A. Sloane
2022-04-13T13:25:17
oeisdata/seq/A005/A005309.seq
9fc7b53c80e65d50e359d6f1a87761ee
A005310
Fermionic string states.
[ "2", "2", "6", "14", "30", "62", "126", "246", "472" ]
[ "nonn" ]
30
0
1
null
[ "M0359" ]
N. J. A. Sloane
2023-08-02T11:44:55
oeisdata/seq/A005/A005310.seq
eff7d1ffe8512a07279962c17773b799
A005311
Solution to Berlekamp's switching game (or lightbulb game) on an n X n board.
[ "0", "1", "2", "4", "7", "11", "16", "22", "27", "35", "43", "54" ]
[ "hard", "nonn", "more", "nice" ]
37
1
3
null
[ "M1040" ]
N. J. A. Sloane
2019-10-27T22:23:59
oeisdata/seq/A005/A005311.seq
7183c5447bc62aa1b66e1a94a911b5ce
A005312
Maximal sum of inverse squares of the singular values of symmetric anti-Hadamard matrices of order n.
[ "1", "3", "7", "16", "46", "138", "624" ]
[ "nonn", "hard", "more" ]
23
1
2
[ "A005312", "A005313" ]
[ "M2659" ]
N. J. A. Sloane.
2022-02-20T22:46:04
oeisdata/seq/A005/A005312.seq
da4f149eca9928ace7f9fcd5a82fd6a2
A005313
Maximal sum of inverse squares of the singular values of triangular anti-Hadamard matrices of order n.
[ "1", "3", "6", "13", "29", "70", "175", "449", "1164", "3035", "7931", "20748", "54301", "142143", "372114", "974185", "2550425", "6677074", "17480779", "45765245", "119814936", "313679543", "821223671", "2149991448", "5628750649", "14736260475", "38580030750", "101003831749", "264431464469", "692290561630", "1812440220391", "4745030099513" ]
[ "nonn", "easy" ]
30
1
2
[ "A005312", "A005313", "A064831" ]
[ "M2573" ]
N. J. A. Sloane.
2022-04-13T13:25:17
oeisdata/seq/A005/A005313.seq
3fdd0dfc17f0e7734a932d95ffa74054
A005314
For n = 0, 1, 2, a(n) = n; thereafter, a(n) = 2*a(n-1) - a(n-2) + a(n-3).
[ "0", "1", "2", "3", "5", "9", "16", "28", "49", "86", "151", "265", "465", "816", "1432", "2513", "4410", "7739", "13581", "23833", "41824", "73396", "128801", "226030", "396655", "696081", "1221537", "2143648", "3761840", "6601569", "11584946", "20330163", "35676949", "62608681", "109870576", "192809420", "338356945", "593775046" ]
[ "nonn", "easy" ]
195
0
3
[ "A003242", "A005251", "A005314", "A011973", "A099557", "A114901", "A224838", "A261041", "A274174" ]
[ "M0709" ]
N. J. A. Sloane
2025-01-22T09:39:01
oeisdata/seq/A005/A005314.seq
f6a79f2a9dc9d492260bdc2d8e4793a7
A005315
Closed meandric numbers (or meanders): number of ways a loop can cross a road 2n times.
[ "1", "1", "2", "8", "42", "262", "1828", "13820", "110954", "933458", "8152860", "73424650", "678390116", "6405031050", "61606881612", "602188541928", "5969806669034", "59923200729046", "608188709574124", "6234277838531806", "64477712119584604", "672265814872772972", "7060941974458061392" ]
[ "nonn", "hard", "nice" ]
109
0
3
[ "A005315", "A005316", "A008828", "A077054", "A077460" ]
[ "M1862" ]
N. J. A. Sloane, J. A. Reeds (reeds(AT)idaccr.org)
2023-10-29T21:50:26
oeisdata/seq/A005/A005315.seq
3522b713736e9cdeb707ba1fe7915aee
A005316
Meandric numbers: number of ways a river can cross a road n times.
[ "1", "1", "1", "2", "3", "8", "14", "42", "81", "262", "538", "1828", "3926", "13820", "30694", "110954", "252939", "933458", "2172830", "8152860", "19304190", "73424650", "176343390", "678390116", "1649008456", "6405031050", "15730575554", "61606881612", "152663683494", "602188541928", "1503962954930", "5969806669034", "15012865733351", "59923200729046", "151622652413194", "608188709574124", "1547365078534578", "6234277838531806", "15939972379349178", "64477712119584604", "165597452660771610", "672265814872772972", "1733609081727968492", "7060941974458061392" ]
[ "nonn", "nice" ]
117
0
4
[ "A005315", "A005316", "A076875", "A076906", "A076907", "A077014", "A077054", "A077055", "A077056", "A078591", "A078592" ]
[ "M0874" ]
N. J. A. Sloane, Stéphane Legendre
2023-10-29T21:50:37
oeisdata/seq/A005/A005316.seq
bc357e3b3f81421b4d30799a82b2c8f7
A005317
a(n) = (2^n + C(2*n,n))/2.
[ "1", "2", "5", "14", "43", "142", "494", "1780", "6563", "24566", "92890", "353740", "1354126", "5204396", "20066492", "77575144", "300572963", "1166868646", "4537698722", "17672894044", "68923788698", "269129985796", "1052051579012", "4116719558104", "16123810230158", "63205319996092", "247959300028484" ]
[ "nonn", "easy" ]
102
0
2
[ "A005317", "A008619", "A108958" ]
[ "M1460" ]
N. J. A. Sloane and Peter Fishburn
2024-12-28T10:18:31
oeisdata/seq/A005/A005317.seq
d1a58d32b22f23e96b47ff2e78cd354d
A005318
Conway-Guy sequence: a(n + 1) = 2a(n) - a(n - floor( 1/2 + sqrt(2n) )).
[ "0", "1", "2", "4", "7", "13", "24", "44", "84", "161", "309", "594", "1164", "2284", "4484", "8807", "17305", "34301", "68008", "134852", "267420", "530356", "1051905", "2095003", "4172701", "8311101", "16554194", "32973536", "65679652", "130828948", "261127540", "521203175", "1040311347", "2076449993", "4144588885", "8272623576" ]
[ "nonn", "easy", "nice" ]
77
0
3
[ "A003056", "A005318", "A037254", "A083920", "A096796", "A096824", "A096858", "A205744", "A206239", "A276661" ]
[ "M1075" ]
N. J. A. Sloane
2024-04-23T16:38:58
oeisdata/seq/A005/A005318.seq
402dff6fc8cc5fd9a1646e6757e98182
A005319
a(n) = 6*a(n-1) - a(n-2).
[ "0", "4", "24", "140", "816", "4756", "27720", "161564", "941664", "5488420", "31988856", "186444716", "1086679440", "6333631924", "36915112104", "215157040700", "1254027132096", "7309005751876", "42600007379160", "248291038523084", "1447146223759344", "8434586304032980" ]
[ "nonn", "easy" ]
134
0
2
[ "A000129", "A001109", "A001541", "A001542", "A001652", "A001653", "A005319", "A046090", "A046729", "A090390" ]
[ "M3599" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005319.seq
217fa88f15398a59b13cccfd65648ba8
A005320
a(n) = 4*a(n-1) - a(n-2), with a(0) = 0, a(1) = 3.
[ "0", "3", "12", "45", "168", "627", "2340", "8733", "32592", "121635", "453948", "1694157", "6322680", "23596563", "88063572", "328657725", "1226567328", "4577611587", "17083879020", "63757904493", "237947738952", "888033051315", "3314184466308", "12368704813917", "46160634789360", "172273834343523", "642934702584732", "2399464975995405", "8954925201396888", "33420235829592147" ]
[ "nonn", "easy" ]
95
0
2
[ "A001075", "A001353", "A002194", "A003500", "A005320", "A082841" ]
[ "M2919" ]
N. J. A. Sloane
2022-10-10T03:55:08
oeisdata/seq/A005/A005320.seq
7749da8f1e4d64e7a7f2d9a1a6c0bc91
A005321
Upper triangular n X n (0,1)-matrices with no zero rows or columns.
[ "1", "1", "2", "10", "122", "3346", "196082", "23869210", "5939193962", "2992674197026", "3037348468846562", "6189980791404487210", "25285903982959247885402", "206838285372171652078912306", "3386147595754801373061066905042", "110909859519858523995273393471390010" ]
[ "nonn", "easy", "nice" ]
92
0
3
[ "A005321", "A022493", "A137252", "A138265", "A289314", "A289315" ]
[ "M1986" ]
N. J. A. Sloane
2024-07-30T09:44:56
oeisdata/seq/A005/A005321.seq
674bcdf451e828b2fa409be0f811ba5b
A005322
Column of Motzkin triangle.
[ "1", "3", "9", "25", "69", "189", "518", "1422", "3915", "10813", "29964", "83304", "232323", "649845", "1822824", "5126520", "14453451", "40843521", "115668105", "328233969", "933206967", "2657946907", "7583013474", "21668135850", "62007732605", "177696228411", "509899901553", "1464990733969", "4214045993925" ]
[ "nonn" ]
70
2
2
[ "A001006", "A005322", "A020474", "A026300" ]
[ "M2799" ]
N. J. A. Sloane
2023-09-12T12:07:32
oeisdata/seq/A005/A005322.seq
6fd4b96cfe53f3c4e2de57b170b0730e
A005323
Column of Motzkin triangle.
[ "1", "4", "14", "44", "133", "392", "1140", "3288", "9438", "27016", "77220", "220584", "630084", "1800384", "5147328", "14727168", "42171849", "120870324", "346757334", "995742748", "2862099185", "8234447672", "23713180780", "68350541480", "197188167735", "569371325796" ]
[ "nonn", "easy" ]
63
3
2
[ "A005323", "A020474", "A026300" ]
[ "M3480" ]
N. J. A. Sloane
2024-01-17T09:07:04
oeisdata/seq/A005/A005323.seq
a1df712868f6d3d5ceb72d54bad4fbfe
A005324
Column of Motzkin triangle A026300.
[ "1", "5", "20", "70", "230", "726", "2235", "6765", "20240", "60060", "177177", "520455", "1524120", "4453320", "12991230", "37854954", "110218905", "320751445", "933149470", "2714401580", "7895719634", "22969224850", "66829893650", "194486929650", "566141346225", "1648500576021" ]
[ "nonn", "easy" ]
61
4
2
[ "A005324", "A020474", "A026300" ]
[ "M3902" ]
N. J. A. Sloane
2022-08-17T10:36:28
oeisdata/seq/A005/A005324.seq
21786d16c1a798766bc049a26b4c090f
A005325
Column of Motzkin triangle.
[ "1", "6", "27", "104", "369", "1242", "4037", "12804", "39897", "122694", "373581", "1128816", "3390582", "10136556", "30192102", "89662216", "265640691", "785509362", "2319218869", "6839057544", "20147488020", "59306494520", "174466248840", "512987904000", "1507780192035", "4430417492826", "13015498076181" ]
[ "nonn" ]
63
5
2
[ "A001006", "A005325", "A020474", "A026126", "A026300" ]
[ "M4176" ]
N. J. A. Sloane
2022-04-13T13:25:17
oeisdata/seq/A005/A005325.seq
78e804fadfdc85921c0e51564957184e
A005326
Permanent of "coprime?" matrix.
[ "1", "1", "3", "4", "28", "16", "256", "324", "3600", "3600", "129744", "63504", "3521232", "3459600", "60891840", "91240704", "8048712960", "3554067456", "425476094976", "320265446400", "12474417291264", "16417666704384", "2778580249611264", "1142807773593600", "172593628397420544" ]
[ "nonn", "nice" ]
64
1
3
[ "A005326", "A009679" ]
[ "M2382" ]
N. J. A. Sloane
2023-03-18T08:49:14
oeisdata/seq/A005/A005326.seq
153d40f0d7abaccf187238ca65bafebc
A005327
Certain subgraphs of a directed graph (inverse binomial transform of A005321).
[ "1", "0", "1", "6", "91", "2820", "177661", "22562946", "5753551231", "2940064679040", "3007686166657921", "6156733583148764286", "25211824022994189751171", "206510050572345408251841660", "3383254158526734823389921915781" ]
[ "nonn" ]
50
1
4
[ "A002820", "A005321", "A005327", "A005329" ]
[ "M4289" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005327.seq
4442994376ab989d03b761cb12bed0e4
A005328
Certain subgraphs of a directed graph.
[ "1", "3", "28", "510", "18631", "1351413", "194192398", "55272612720", "31184369778961", "34909296450535023", "77616063417393956368", "343049603717222441078130", "3016429354620114423122804491", "52801416275268069417410827891833" ]
[ "nonn" ]
19
2
2
null
[ "M3118" ]
N. J. A. Sloane
2017-09-04T00:22:48
oeisdata/seq/A005/A005328.seq
942a4d942380d493c81e7c3ab0ed63cb
A005329
a(n) = Product_{i=1..n} (2^i - 1). Also called 2-factorial numbers.
[ "1", "1", "3", "21", "315", "9765", "615195", "78129765", "19923090075", "10180699028325", "10414855105976475", "21319208401933844325", "87302158405919092510875", "715091979502883286756577125", "11715351900195736886933003038875", "383876935713713710574133710574817125" ]
[ "nonn", "easy", "nice" ]
159
0
3
[ "A000225", "A005321", "A005329", "A006088", "A006125", "A027871", "A027872", "A027873", "A028362", "A032085", "A048651", "A048652", "A069777", "A075271", "A075272", "A079555", "A114604", "A122746", "A152476" ]
[ "M3085" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005329.seq
4b8e9ea980a9edb507a651943d625058
A005330
Certain subgraphs of a directed graph.
[ "1", "5", "40", "644", "21496", "1471460", "204062440", "56865072164", "31688930152696", "35223651007587140", "78001790003385408040", "343983307379873262633284", "3020895063527811952260491896", "52843677532033943174017588842020", "1841795434229559227318546660111716840" ]
[ "nonn" ]
23
2
2
null
[ "M3992" ]
N. J. A. Sloane
2024-12-28T02:01:19
oeisdata/seq/A005/A005330.seq
15011a96cb0795ade71b3cacdb1ff4f1
A005331
Certain subgraphs of a directed graph (binomial transform of A005321).
[ "1", "2", "5", "20", "179", "4082", "218225", "25316720", "6135834479", "3047003143022", "3067545380897645", "6223557209578656620", "25360384878802358268779", "207167485813280961035481962", "3389045635023473628621934703465", "110960673463328354866093662279119720", "7268699514166911556909103208203294815079" ]
[ "nonn" ]
23
0
2
null
[ "M1531" ]
N. J. A. Sloane.
2021-04-13T18:40:13
oeisdata/seq/A005/A005331.seq
266a344cea6bdcd3a22eb0276a569ec7
A005332
Certain subgraphs of a directed graph.
[ "1", "7", "58", "838", "25171", "1610977", "214838128", "58540023808", "32208188445841", "35543124039418147", "78391002506394742198", "344921660620756227029578", "3025372940760065880037836511", "52886001393832278158415800800117", "1842588406743140390123203185385824268", "127974225758895121562137768141145597226148" ]
[ "nonn" ]
25
2
2
[ "A005330", "A005332" ]
[ "M4438" ]
N. J. A. Sloane
2024-12-28T02:01:15
oeisdata/seq/A005/A005332.seq
d275469ec29455a64c38d23834bd5813
A005333
Number of 2-colored connected labeled graphs with n vertices of the first color and n vertices of the second color.
[ "1", "5", "205", "36317", "23679901", "56294206205", "502757743028605", "17309316971673776957", "2333508400614646874734621", "1243000239291173897659593056765", "2629967962392578020413552363565293565", "22170252073745058975210005804934596601690557" ]
[ "nonn" ]
40
1
2
[ "A005333", "A227322", "A262307" ]
[ "M4030" ]
N. J. A. Sloane
2022-10-25T20:30:12
oeisdata/seq/A005/A005333.seq
bf42507cfc624605c0c7f07d9132b6ea
A005334
Number of labeled nonseparable (or 2-connected) bicolored graphs with n nodes of the first color and n nodes of the second color.
[ "1", "1", "34", "7037", "6317926", "21073662977", "251973418941994", "10878710974408306717", "1727230695707098000548430", "1028983422758641650604161840065", "2342608062302306704492272616530549874", "20683716767972841770515007707311751484424893" ]
[ "nonn" ]
24
1
3
[ "A005333", "A005334", "A005335", "A005336", "A123301" ]
[ "M5244" ]
N. J. A. Sloane
2021-01-08T21:16:14
oeisdata/seq/A005/A005334.seq
a556a68ce09920a689307fb55e984778
A005335
Number of labeled nonseparable (or 2-connected) bipartite graphs with 2n nodes and n nodes in each part.
[ "1", "3", "340", "246295", "796058676", "9736032295374", "432386386904461704", "70004505120317453723895", "41988978212639552393332333300", "95055430627597798399511262461524570", "826275345303020411581696428212189429357784", "27965998400207183955394390590886658323558240477654" ]
[ "nonn" ]
20
1
2
[ "A005334", "A005335", "A123474" ]
[ "M3177" ]
N. J. A. Sloane
2021-01-04T16:56:56
oeisdata/seq/A005/A005335.seq
78a831d0fca1dd3369c6e2a2f129b144
A005336
Number of labeled nonseparable (or 2-connected) bipartite graphs with 2n nodes.
[ "1", "3", "355", "297619", "1120452771", "15350524923547", "738416821509929731", "126430202628042630866787", "78847417416749666369637926851", "183373380693566591129149674727445419", "1623847327688450079238401833083018045926051", "55669578575421273854874611540671620662810228887603" ]
[ "nonn" ]
15
1
2
[ "A004100", "A005334", "A005335", "A005336" ]
[ "M3178" ]
N. J. A. Sloane
2021-01-04T14:09:04
oeisdata/seq/A005/A005336.seq
cb6bb7314e77d4541115d92edead7ad4
A005337
Number of ways in which n identical balls can be distributed among 4 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.
[ "15", "40", "76", "124", "185", "260", "350", "456", "579", "720", "880", "1060", "1261", "1484", "1730", "2000", "2295", "2616", "2964", "3340", "3745", "4180", "4646", "5144", "5675", "6240", "6840", "7476", "8149", "8860", "9610", "10400", "11231", "12104", "13020", "13980", "14985" ]
[ "nonn", "easy" ]
52
8
1
[ "A005337", "A005338", "A005339", "A005340", "A259975" ]
[ "M4963" ]
N. J. A. Sloane, Simon Plouffe
2022-04-13T13:25:17
oeisdata/seq/A005/A005337.seq
362c43b0ad1fd83c073294f2ef9f2374
A005338
Number of ways in which n identical balls can be distributed among 5 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.
[ "1", "8", "31", "85", "190", "360", "610", "956", "1415", "2005", "2745", "3655", "4756", "6070", "7620", "9430", "11525", "13931", "16675", "19785", "23290", "27220", "31606", "36480", "41875", "47825", "54365", "61531", "69360", "77890", "87160", "97210", "108081", "119815", "132455", "146045", "160630" ]
[ "nonn", "easy" ]
51
8
2
[ "A005337", "A005338", "A005339", "A005340" ]
[ "M4508" ]
N. J. A. Sloane
2022-09-08T08:44:33
oeisdata/seq/A005/A005338.seq
272d477caac7d017d4e32f0effbf47c1
A005339
Number of ways in which n identical balls can be distributed among 6 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.
[ "35", "154", "424", "930", "1775", "3080", "4985", "7650", "11256", "16006", "22126", "29866", "39501", "51332", "65687", "82922", "103422", "127602", "155908", "188818", "226843", "270528", "320453", "377234", "441524", "514014", "595434", "686554", "788185", "901180", "1026435", "1164890", "1317530" ]
[ "nonn", "easy" ]
38
12
1
[ "A005337", "A005338", "A005339", "A005340" ]
[ "M5245" ]
N. J. A. Sloane
2021-03-23T21:26:59
oeisdata/seq/A005/A005339.seq
837aeaccd5dcd35f2a0d503c15fab27d
A005340
Number of ways in which n identical balls can be distributed among 7 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.
[ "1", "13", "76", "295", "889", "2188", "4652", "8891", "15686", "26011", "41056", "62251", "91291", "130162", "181168", "246959", "330560", "435401", "565348", "724735", "918397", "1151704", "1430596", "1761619", "2151962", "2609495", "3142808", "3761251", "4474975", "5294974", "6233128" ]
[ "nonn", "easy" ]
52
12
2
[ "A005337", "A005338", "A005339", "A005340" ]
[ "M4903" ]
N. J. A. Sloane
2025-04-03T10:47:32
oeisdata/seq/A005/A005340.seq
dc1b34636f406e10279b173afd4c8644
A005341
Length of n-th term in Look and Say sequences A005150 and A007651.
[ "1", "2", "2", "4", "6", "6", "8", "10", "14", "20", "26", "34", "46", "62", "78", "102", "134", "176", "226", "302", "408", "528", "678", "904", "1182", "1540", "2012", "2606", "3410", "4462", "5808", "7586", "9898", "12884", "16774", "21890", "28528", "37158", "48410", "63138", "82350", "107312", "139984", "182376", "237746", "310036", "403966", "526646", "686646" ]
[ "nonn", "base", "easy", "nice" ]
62
1
2
null
[ "M0321" ]
Jeffrey Shallit
2025-02-16T08:32:28
oeisdata/seq/A005/A005341.seq
e70ed3ef69a6a6855baa3afc61c98c8b
A005342
a(n) = solution to the postage stamp problem with n denominations and 7 stamps.
[ "7", "23", "69", "165", "345", "664", "1137", "1911" ]
[ "nonn", "more" ]
24
1
1
[ "A001208", "A001209", "A001210", "A001211", "A001212", "A001213", "A001214", "A001215", "A001216", "A005342", "A005343", "A005344", "A014616", "A053346", "A053348", "A075060", "A084192", "A084193" ]
[ "M4380" ]
N. J. A. Sloane.
2020-08-14T13:45:30
oeisdata/seq/A005/A005342.seq
c91607fce8092d597302f0916a1394d5
A005343
a(n) = solution to the postage stamp problem with n denominations and 8 stamps.
[ "8", "28", "89", "234", "512", "1045", "2001", "3485" ]
[ "nonn", "more" ]
24
1
1
[ "A001208", "A001209", "A001210", "A001211", "A001212", "A001213", "A001214", "A001215", "A001216", "A005342", "A005343", "A005344", "A014616", "A053346", "A053348", "A075060", "A084192", "A084193" ]
[ "M4505" ]
N. J. A. Sloane.
2020-08-14T13:46:00
oeisdata/seq/A005/A005343.seq
94f6898705ec48db2f71c4111eaca728
A005344
a(n) = solution to the postage stamp problem with n denominations and 9 stamps.
[ "9", "34", "112", "326", "797", "1617", "3191" ]
[ "nonn", "more" ]
23
1
1
[ "A001208", "A001209", "A001210", "A001211", "A001212", "A001213", "A001214", "A001215", "A001216", "A005342", "A005343", "A005344", "A014616", "A053346", "A053348", "A075060", "A084192", "A084193" ]
[ "M4615" ]
N. J. A. Sloane.
2020-08-14T13:46:29
oeisdata/seq/A005/A005344.seq
a77d415843437d44c257e47c3b5cf944
A005345
Number of elements of a free idempotent monoid on n letters.
[ "1", "2", "7", "160", "332381", "2751884514766", "272622932796281408879065987", "3641839910835401567626683593436003894250931310990279692", "848831867913830760986671126293000918118297635181600248839480614255059539078136221019132415247551725144817958905" ]
[ "nonn", "easy" ]
28
0
2
[ "A005345", "A030449" ]
[ "M1820" ]
N. J. A. Sloane, Jeffrey Shallit
2025-02-16T08:32:28
oeisdata/seq/A005/A005345.seq
24076b6a22728e0ba5388f95b577ac59
A005346
Van der Waerden numbers W(2,n).
[ "1", "3", "9", "35", "178", "1132" ]
[ "nonn", "hard", "more" ]
67
1
2
[ "A005346", "A121894" ]
[ "M2819" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005346.seq
46ef413c9cf92b8840bc7949004ddfb4
A005347
First differences of A005579.
[ "1", "1", "1", "1", "2", "3", "5", "8", "13", "20", "34", "53", "88", "143", "236", "387", "641", "1061", "1763", "2937", "4903", "8202", "13750", "23095", "38850", "65461", "110465", "186665", "315827", "535011", "907341", "1540416", "2617782", "4452846", "7581016", "12917486", "22027745", "37591270", "64196610" ]
[ "nonn", "nice", "changed" ]
49
0
5
[ "A000045", "A005347", "A005579" ]
[ "M0690" ]
N. J. A. Sloane, R. K. Guy, Apr 12 1988
2025-04-18T09:57:37
oeisdata/seq/A005/A005347.seq
2544767471f436bb6c1cf3036148e1e9
A005348
Number of ways to add n ordinals.
[ "1", "2", "5", "13", "33", "81", "193", "449", "1089", "2673", "6561", "15633", "37249", "88209", "216513", "531441", "1266273", "3017169", "7189057", "17537553", "43046721", "102568113", "244390689", "582313617", "1420541793", "3486784401", "8308017153", "19795645809", "47167402977", "115063885233", "282429536481" ]
[ "nonn", "easy" ]
51
1
2
null
[ "M1435" ]
N. J. A. Sloane, R. K. Guy, Bill Sands and Tommy Kucera
2025-03-23T23:27:40
oeisdata/seq/A005/A005348.seq
f50c1cc7d42defb665e2684344b66c11
A005349
Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "18", "20", "21", "24", "27", "30", "36", "40", "42", "45", "48", "50", "54", "60", "63", "70", "72", "80", "81", "84", "90", "100", "102", "108", "110", "111", "112", "114", "117", "120", "126", "132", "133", "135", "140", "144", "150", "152", "153", "156", "162", "171", "180", "190", "192", "195", "198", "200", "201", "204" ]
[ "nonn", "base", "nice", "easy", "changed" ]
182
1
2
[ "A001101", "A001102", "A005349", "A007602", "A007953", "A028834", "A038186", "A049445", "A052018", "A052019", "A052020", "A052021", "A052022", "A065877", "A070635", "A113315", "A118363", "A141769", "A154701", "A188641", "A330927", "A330928", "A330929", "A330930" ]
[ "M0481" ]
N. J. A. Sloane, Robert G. Wilson v
2025-04-21T02:26:10
oeisdata/seq/A005/A005349.seq
f519ee3ff63075bc97adcd432c7eb38f
A005350
a(1) = a(2) = a(3) = 1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n >= 4.
[ "1", "1", "1", "2", "2", "3", "3", "3", "4", "5", "5", "5", "5", "6", "7", "7", "8", "8", "8", "8", "8", "9", "10", "11", "11", "12", "12", "12", "13", "13", "13", "13", "13", "13", "14", "15", "16", "16", "17", "18", "18", "19", "19", "19", "20", "20", "20", "20", "21", "21", "21", "21", "21", "21", "21", "22", "23", "24", "25", "25", "26", "27", "27", "28" ]
[ "nonn", "easy", "nice" ]
41
1
4
[ "A004001", "A005185", "A005350", "A005707" ]
[ "M0253" ]
N. J. A. Sloane, R. K. Guy
2024-03-27T08:40:44
oeisdata/seq/A005/A005350.seq
1d17c6dc8d1fd3d8b74559c7bfa14342
A005351
Base -2 representation for n regarded as base 2, then evaluated.
[ "0", "1", "6", "7", "4", "5", "26", "27", "24", "25", "30", "31", "28", "29", "18", "19", "16", "17", "22", "23", "20", "21", "106", "107", "104", "105", "110", "111", "108", "109", "98", "99", "96", "97", "102", "103", "100", "101", "122", "123", "120", "121", "126", "127", "124", "125", "114", "115", "112", "113", "118", "119", "116", "117", "74", "75", "72", "73", "78", "79", "76" ]
[ "nonn", "base", "easy", "nice", "look" ]
74
0
3
[ "A000120", "A005351", "A005352", "A029931", "A035327", "A039724", "A053985", "A065359", "A070939", "A185269", "A326032" ]
[ "M4059" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005351.seq
25702c6e9ff7182e1346cea04c70ea90
A005352
Base -2 representation of -n reinterpreted as binary.
[ "3", "2", "13", "12", "15", "14", "9", "8", "11", "10", "53", "52", "55", "54", "49", "48", "51", "50", "61", "60", "63", "62", "57", "56", "59", "58", "37", "36", "39", "38", "33", "32", "35", "34", "45", "44", "47", "46", "41", "40", "43", "42", "213", "212", "215", "214", "209", "208", "211", "210", "221", "220", "223", "222", "217", "216", "219", "218", "197", "196", "199", "198", "193", "192", "195", "194", "205", "204", "207", "206", "201", "200" ]
[ "nonn", "base", "nice", "look" ]
64
1
1
[ "A005351", "A005352", "A212529" ]
[ "M2259" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005352.seq
9aa7903502bc42cd89d36a09ba59b056
A005353
Number of 2 X 2 matrices with entries mod n and nonzero determinant.
[ "0", "6", "48", "168", "480", "966", "2016", "3360", "5616", "8550", "13200", "17832", "26208", "34566", "45840", "59520", "78336", "95526", "123120", "147240", "181776", "219846", "267168", "307488", "372000", "433446", "505440", "580776", "682080", "762150", "892800", "999936", "1138368", "1284486" ]
[ "nonn", "easy", "nice" ]
29
1
2
[ "A005353", "A020478", "A059306", "A062801" ]
[ "M4254" ]
N. J. A. Sloane, R. K. Guy
2023-10-31T04:45:23
oeisdata/seq/A005/A005353.seq
bdf1257cdeb1a442c07e27f6eaa7964e
A005354
Number of asymmetric planar trees with n nodes.
[ "1", "1", "0", "0", "0", "1", "3", "9", "28", "85", "262", "827", "2651", "8626", "28507", "95393", "322938", "1104525", "3812367", "13266366", "46504495", "164098390", "582521687", "2079133141", "7457788295", "26872946466", "97238824018", "353218128299", "1287657977946", "4709784136316" ]
[ "nonn", "nice" ]
48
0
7
[ "A000108", "A002995", "A005354", "A022553" ]
[ "M2808" ]
N. J. A. Sloane, Simon Plouffe, Susanna Cuyler
2018-01-31T10:52:38
oeisdata/seq/A005/A005354.seq
efd97b35ba5d4e83c77b5e23fdc90586
A005355
Number of asymmetric permutation rooted trees with n nodes.
[ "0", "1", "1", "1", "3", "7", "21", "61", "187", "577", "1825", "5831", "18883", "61699", "203429", "675545", "2258291", "7592249", "25656477", "87096661", "296891287", "1015797379", "3487272317", "12008898531", "41471260883", "143588078449", "498343911529", "1733410858955", "6041795275027", "21098924740155" ]
[ "nonn", "nice", "easy", "eigen" ]
27
0
5
[ "A004111", "A005355", "A050383" ]
[ "M2680" ]
N. J. A. Sloane, Simon Plouffe, Susanna Cuyler
2018-06-22T23:07:39
oeisdata/seq/A005/A005355.seq
bd442ed0df015e01ac38195d50894913
A005356
Number of low discrepancy sequences in base 2.
[ "0", "0", "1", "3", "5", "8", "11", "14", "18", "22", "26", "30", "34", "38", "43", "48", "53", "58", "63", "68", "73", "78", "83", "89", "95", "101", "107", "113", "119", "125", "131", "137", "143", "149", "155", "161", "167", "173", "179", "185", "191", "198", "205", "212", "219", "226", "233", "240", "247", "254", "261", "268", "275", "282", "289", "296" ]
[ "nonn" ]
30
1
4
[ "A005356", "A005357", "A005358", "A005377" ]
[ "M2435" ]
N. J. A. Sloane, Simon Plouffe
2023-03-09T08:04:53
oeisdata/seq/A005/A005356.seq
7c0eb25254116a320ab1a62f72188139
A005357
Number of low discrepancy sequences in base 3.
[ "0", "0", "0", "1", "2", "3", "5", "7", "9", "11", "13", "15", "17", "19", "22", "25", "28", "31", "34", "37", "40", "43", "46", "49", "52", "55", "58", "61", "64", "67", "70", "73", "77", "81", "85", "89", "93", "97", "101", "105", "109", "113", "117", "121", "125", "129", "133", "137", "141", "145", "149", "153", "157", "161", "165", "169", "173", "177" ]
[ "nonn" ]
28
1
5
[ "A005356", "A005357", "A005358", "A005377" ]
[ "M0637" ]
N. J. A. Sloane, Simon Plouffe
2023-09-13T09:43:30
oeisdata/seq/A005/A005357.seq
5d031d27a6dff8db30d5ba3574d3b5a8
A005358
Number of low discrepancy sequences in base 5.
[ "0", "0", "0", "0", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "16", "18", "20", "22", "24", "26", "28", "30", "32", "34", "36", "38", "40", "42", "44", "46", "48", "50", "52", "54", "56", "58", "60", "62", "64", "66", "68", "70", "72", "74", "76", "78", "80", "82", "84", "86", "88", "90", "93", "96", "99", "102", "105", "108", "111", "114", "117", "120", "123", "126", "129", "132", "135", "138", "141", "144", "147", "150", "153", "156", "159", "162" ]
[ "nonn" ]
31
1
7
[ "A005356", "A005357", "A005358", "A005377" ]
[ "M0478" ]
N. J. A. Sloane, Simon Plouffe
2023-09-13T09:43:20
oeisdata/seq/A005/A005358.seq
742c896583ecde3c49b012ab962778ee
A005359
a(n) = n! if n is even, otherwise 0 (from Taylor series for cos x).
[ "1", "0", "2", "0", "24", "0", "720", "0", "40320", "0", "3628800", "0", "479001600", "0", "87178291200", "0", "20922789888000", "0", "6402373705728000", "0", "2432902008176640000", "0", "1124000727777607680000", "0", "620448401733239439360000", "0" ]
[ "nonn" ]
51
0
3
[ "A005359", "A010050", "A167565", "A167568", "A177145" ]
null
N. J. A. Sloane, Russ Cox
2022-08-12T19:59:28
oeisdata/seq/A005/A005359.seq
e1f261673511e94b8086350a6554803f
A005360
Flimsy numbers.
[ "11", "13", "19", "22", "23", "25", "26", "27", "29", "37", "38", "39", "41", "43", "44", "46", "47", "50", "52", "53", "54", "55", "57", "58", "59", "61", "67", "71", "74", "76", "77", "78", "79", "81", "82", "83", "86", "87", "88", "91", "92", "94", "95", "97", "99", "100", "101", "103", "104", "106", "107", "108", "109", "110", "111", "113", "114", "115", "116", "117", "118", "119", "121" ]
[ "nonn", "nice", "base" ]
49
1
1
[ "A000120", "A005360", "A125121" ]
[ "M4771" ]
Jeffrey Shallit
2020-06-04T11:58:34
oeisdata/seq/A005/A005360.seq
0ced06ae6e4856f87567f28c7db6ebae
A005361
Product of exponents of prime factorization of n.
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "4", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "5", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "4", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "6", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1" ]
[ "nonn", "easy", "nice", "mult" ]
141
1
4
[ "A000005", "A002110", "A005117", "A005361", "A028234", "A052306", "A067029", "A072411", "A082695", "A284318", "A340065", "A360969", "A360970", "A361132" ]
[ "M0063" ]
Jeffrey Shallit and Olivier Gérard
2024-01-28T09:02:19
oeisdata/seq/A005/A005361.seq
aba4a453b9442a29be1faffb39f11252
A005362
Hoggatt sequence with parameter d=4.
[ "1", "2", "7", "32", "177", "1122", "7898", "60398", "494078", "4274228", "38763298", "366039104", "3579512809", "36091415154", "373853631974", "3966563630394", "42997859838010", "475191259977060", "5344193918791710", "61066078557804360", "707984385321707910", "8318207051955884772", "98936727936728464152" ]
[ "nonn" ]
62
0
2
[ "A005362", "A005364", "A005365", "A005366", "A056940", "A116925" ]
[ "M1789" ]
N. J. A. Sloane, Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005362.seq
dc5ffe15b9988073133ba2647695571d
A005363
Hoggatt sequence with parameter d=5.
[ "1", "2", "8", "44", "310", "2606", "25202", "272582", "3233738", "41454272", "567709144", "8230728508", "125413517530", "1996446632130", "33039704641922", "566087847780250", "10006446665899330", "181938461947322284", "3393890553702212368", "64807885247524512668", "1264344439859632559216" ]
[ "nonn" ]
63
0
2
[ "A000079", "A000108", "A001181", "A005362", "A005363", "A005364", "A005365", "A005366", "A056941", "A116925" ]
[ "M1867" ]
N. J. A. Sloane, Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005363.seq
3af209917c9aa62d80d68dfc024638ff
A005364
Hoggatt sequence with parameter d=6.
[ "1", "2", "9", "58", "506", "5462", "70226", "1038578", "17274974", "317292692", "6346909285", "136723993122", "3143278648954", "76547029418394", "1962350550273130", "52679691605422354", "1474290522744355250", "42847373913958703100", "1288899422418558314550", "40013380588722843337620" ]
[ "nonn" ]
70
0
2
[ "A000079", "A000108", "A001181", "A005362", "A005363", "A005364", "A005365", "A005366", "A116925", "A142465" ]
[ "M1943" ]
N. J. A. Sloane
2024-09-16T06:40:30
oeisdata/seq/A005/A005364.seq
90b72acb45496c9c874de8d9ae2e7320
A005365
Hoggatt sequence with parameter d=7.
[ "1", "2", "10", "74", "782", "10562", "175826", "3457742", "78408332", "2005691690", "56970282514", "1772967273794", "59814500606018", "2168062920325850", "83802728579860658", "3432438439271783026", "148165335791410936770", "6708873999658599592672" ]
[ "nonn" ]
68
0
2
[ "A000079", "A000108", "A001181", "A005362", "A005363", "A005364", "A005365", "A005366", "A116925", "A142467" ]
[ "M1976" ]
N. J. A. Sloane
2024-09-16T06:39:57
oeisdata/seq/A005/A005365.seq
cbc7a17ce0908af973156893d453225e
A005366
Hoggatt sequence with parameter d=8.
[ "1", "2", "11", "92", "1157", "19142", "403691", "10312304", "311348897", "10826298914", "426196716090", "18700516849302", "903666922873158", "47592378143008974", "2708388575679431454", "165309083872549538190", "10753269337589887334670", "741379205762167719365268" ]
[ "nonn" ]
73
0
2
[ "A000079", "A000108", "A001181", "A005362", "A005363", "A005364", "A005365", "A005366", "A116925", "A142468" ]
[ "M2006" ]
N. J. A. Sloane
2024-09-15T17:15:32
oeisdata/seq/A005/A005366.seq
cfe765a0728f879fc674aa1f286ca8c8
A005367
a(n) = 2*(2^n + 1)*(2^(n+1) - 1).
[ "4", "18", "70", "270", "1054", "4158", "16510", "65790", "262654", "1049598", "4196350", "16781310", "67117054", "268451838", "1073774590", "4295032830", "17180000254", "68719738878", "274878431230", "1099512676350", "4398048608254", "17592190238718", "70368752566270", "281474993487870", "1125899940397054" ]
[ "nonn", "easy" ]
35
0
1
[ "A005367", "A092431" ]
null
N. J. A. Sloane
2024-02-02T19:24:49
oeisdata/seq/A005/A005367.seq
6009fedc4d43c34736832446e49546f4
A005368
Occurrences of principal character.
[ "1", "0", "1", "3", "6", "15", "42", "109", "320", "979", "3137", "10603", "37728", "140423", "546859", "2220294", "9374309", "41059926", "186149869", "871717073", "4208841555", "20917405824", "106849492793" ]
[ "nonn", "more" ]
30
0
4
[ "A000664", "A005368", "A259976", "A331509" ]
[ "M2589" ]
N. J. A. Sloane
2025-01-20T16:25:42
oeisdata/seq/A005/A005368.seq
922521ea8a0f01dab98876c32700b4b1
A005369
a(n) = 1 if n is of the form m(m+1), else 0.
[ "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "easy" ]
60
0
1
[ "A000194", "A002378", "A005369", "A010052", "A010054", "A016813", "A240025" ]
null
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005369.seq
e2ff3366de7a6301313b5ca6ca39d043
A005370
a(n) = Fibonacci(Fibonacci(n+1) + 1).
[ "1", "1", "2", "3", "8", "34", "377", "17711", "9227465", "225851433717", "2880067194370816120", "898923707008479989274290850145", "3577855662560905981638959513147239988861837901112", "4444705723234237498833973519982908519933430818636409166351397897095281987215864" ]
[ "nonn" ]
38
0
3
[ "A000045", "A005370", "A007570" ]
[ "M0891" ]
N. J. A. Sloane
2022-11-15T02:41:39
oeisdata/seq/A005/A005370.seq
a637ed84800a107069b699c5a7020124
A005371
a(n) = L(L(n)), where L(n) are Lucas numbers A000032.
[ "3", "1", "4", "7", "29", "199", "5778", "1149851", "6643838879", "7639424778862807", "50755107359004694554823204", "387739824812222466915538827541705412334749", "19679776435706023589554719270187913247121278789615838446937339578603" ]
[ "easy", "nonn" ]
59
0
1
[ "A000032", "A005371", "A005372", "A007570", "A068096", "A068098" ]
[ "M3315" ]
N. J. A. Sloane
2023-07-03T05:14:08
oeisdata/seq/A005/A005371.seq
4c319aebaaf4b873c2066509c3116a8f
A005372
a(n) = L(L(n+1)+1), where L(n) are Lucas numbers A000032.
[ "3", "7", "11", "47", "322", "9349", "1860498", "10749957122", "12360848946698171", "82123488809519507169850807", "627376215338105766356982006981782561278127", "31842547163971605907183271059340725709462269514762215168643703957079" ]
[ "nonn" ]
28
0
1
[ "A000032", "A005371", "A005372" ]
[ "M2628" ]
N. J. A. Sloane
2022-11-15T02:41:42
oeisdata/seq/A005/A005372.seq
a9bf001c6c9b46b0136ad12be8b0e0f8
A005373
A class of rooted trees with n nodes.
[ "1", "3", "21", "231", "3495", "67455", "1584765", "43897455", "1400923755", "50619052575", "2042745514425", "91066568444775", "4444738893770175", "235731740255186175", "13499365993279291125", "830161812269496081375", "54564569247212367217875", "3817309552613869238301375" ]
[ "nonn" ]
21
1
2
null
[ "M3083" ]
N. J. A. Sloane.
2017-06-29T19:29:20
oeisdata/seq/A005/A005373.seq
d912755268cfec17332ddb661613b191
A005374
Hofstadter H-sequence: a(n) = n - a(a(a(n-1))).
[ "0", "1", "1", "2", "3", "4", "4", "5", "5", "6", "7", "7", "8", "9", "10", "10", "11", "12", "13", "13", "14", "14", "15", "16", "17", "17", "18", "18", "19", "20", "20", "21", "22", "23", "23", "24", "24", "25", "26", "26", "27", "28", "29", "29", "30", "31", "32", "32", "33", "33", "34", "35", "35", "36", "37", "38", "38", "39", "40", "41", "41", "42", "42", "43", "44", "45", "45", "46", "46", "47", "48", "48", "49", "50" ]
[ "nonn", "nice" ]
110
0
4
[ "A005374", "A202340", "A202341", "A202342" ]
[ "M0449" ]
N. J. A. Sloane
2025-04-02T04:14:04
oeisdata/seq/A005/A005374.seq
2989c80f1df15748183215a5d24f292a
A005375
a(0) = 0; a(n) = n - a(a(a(a(n-1)))) for n > 0.
[ "0", "1", "1", "2", "3", "4", "5", "5", "6", "6", "7", "8", "8", "9", "10", "11", "11", "12", "13", "14", "15", "15", "16", "17", "18", "19", "19", "20", "20", "21", "22", "23", "24", "24", "25", "25", "26", "27", "27", "28", "29", "30", "31", "31", "32", "32", "33", "34", "34", "35", "36", "37", "37", "38", "39", "40", "41", "41", "42", "42", "43", "44", "44", "45", "46", "47", "47", "48", "49", "50", "51", "51", "52", "53" ]
[ "nonn", "nice" ]
66
0
4
null
[ "M0458" ]
N. J. A. Sloane
2025-03-07T11:39:51
oeisdata/seq/A005/A005375.seq
5fe9cc860f6b5c565bae1ca7a323dd8f
A005376
a(n) = n - a(a(a(a(a(n-1))))).
[ "0", "1", "1", "2", "3", "4", "5", "6", "6", "7", "7", "8", "9", "9", "10", "11", "12", "12", "13", "14", "15", "16", "16", "17", "18", "19", "20", "21", "21", "22", "23", "24", "25", "26", "26", "27", "27", "28", "29", "30", "31", "32", "32", "33", "33", "34", "35", "35", "36", "37", "38", "39", "40", "40", "41", "41", "42", "43", "43", "44", "45", "46", "46", "47", "48", "49", "50", "51", "51", "52", "52", "53", "54", "54" ]
[ "nonn" ]
58
0
4
[ "A005206", "A005374", "A005375", "A005376", "A100721" ]
[ "M0464" ]
N. J. A. Sloane
2025-03-15T15:36:19
oeisdata/seq/A005/A005376.seq
a0bb077173f7e05f3b84219b38c22d91
A005377
Number of low discrepancy sequences in base 4.
[ "0", "0", "0", "0", "1", "2", "3", "4", "5", "6", "8", "10", "12", "14", "16", "18", "20", "22", "24", "26", "28", "30", "32", "34", "36", "38", "40", "42", "44", "46", "49", "52", "55", "58", "61", "64", "67", "70", "73", "76", "79", "82", "85", "88", "91", "94", "97", "100", "103", "106", "109", "112", "115", "118", "121", "124", "127", "130", "133", "136", "139" ]
[ "nonn", "easy" ]
32
1
6
[ "A001037", "A005356", "A005357", "A005358", "A005377", "A027376", "A027377", "A062692", "A114945", "A114946", "A274039" ]
[ "M0504" ]
N. J. A. Sloane, Simon Plouffe
2023-09-12T12:02:28
oeisdata/seq/A005/A005377.seq
d9e64d9ef16b909d02262bbff13f4ec6
A005378
The female of a pair of recurrences.
[ "1", "1", "2", "2", "3", "3", "4", "5", "5", "6", "6", "7", "8", "8", "9", "9", "10", "11", "11", "12", "13", "13", "14", "14", "15", "16", "16", "17", "17", "18", "19", "19", "20", "21", "21", "22", "22", "23", "24", "24", "25", "25", "26", "27", "27", "28", "29", "29", "30", "30", "31", "32", "32", "33", "34", "34", "35", "35", "36", "37", "37", "38", "38", "39", "40", "40", "41", "42", "42", "43", "43", "44", "45", "45" ]
[ "nonn", "nice", "easy" ]
69
0
3
[ "A005378", "A005379" ]
[ "M0263" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005378.seq
38e54cefe08edb902adca93f7472c4d7
A005379
The male of a pair of recurrences.
[ "0", "0", "1", "2", "2", "3", "4", "4", "5", "6", "6", "7", "7", "8", "9", "9", "10", "11", "11", "12", "12", "13", "14", "14", "15", "16", "16", "17", "17", "18", "19", "19", "20", "20", "21", "22", "22", "23", "24", "24", "25", "25", "26", "27", "27", "28", "29", "29", "30", "30", "31", "32", "32", "33", "33", "34", "35", "35", "36", "37", "37", "38", "38", "39", "40", "40", "41", "42", "42", "43", "43", "44", "45", "45" ]
[ "nonn", "nice", "easy" ]
83
0
4
[ "A005378", "A005379" ]
[ "M0278" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005379.seq
2ac89a0ef7b2c2284f43eb9988142048
A005380
Expansion of 1 / Product_{k>=1} (1-x^k)^(k+1).
[ "1", "2", "6", "14", "33", "70", "149", "298", "591", "1132", "2139", "3948", "7199", "12894", "22836", "39894", "68982", "117948", "199852", "335426", "558429", "922112", "1511610", "2460208", "3977963", "6390942", "10206862", "16207444", "25596941", "40214896", "62868772", "97814358" ]
[ "nonn", "easy", "nice" ]
102
0
2
[ "A000219", "A005380", "A054225", "A075196", "A089353", "A217093", "A219555", "A255050", "A255052", "A298988" ]
[ "M1601" ]
N. J. A. Sloane
2021-05-28T06:03:03
oeisdata/seq/A005/A005380.seq
57b64977fc4826475b108e77b30f7b18
A005381
Numbers k such that k and k-1 are composite.
[ "9", "10", "15", "16", "21", "22", "25", "26", "27", "28", "33", "34", "35", "36", "39", "40", "45", "46", "49", "50", "51", "52", "55", "56", "57", "58", "63", "64", "65", "66", "69", "70", "75", "76", "77", "78", "81", "82", "85", "86", "87", "88", "91", "92", "93", "94", "95", "96", "99", "100", "105", "106", "111", "112", "115", "116", "117", "118", "119", "120", "121", "122" ]
[ "nonn", "easy" ]
47
1
1
[ "A005381", "A007921", "A068780", "A093515", "A323162" ]
[ "M4598" ]
N. J. A. Sloane
2022-09-18T11:06:20
oeisdata/seq/A005/A005381.seq
024a23ccdde0ba7ce78f7b01d431c54f
A005382
Primes p such that 2p-1 is also prime.
[ "2", "3", "7", "19", "31", "37", "79", "97", "139", "157", "199", "211", "229", "271", "307", "331", "337", "367", "379", "439", "499", "547", "577", "601", "607", "619", "661", "691", "727", "811", "829", "877", "937", "967", "997", "1009", "1069", "1171", "1237", "1279", "1297", "1399", "1429", "1459", "1531", "1609", "1627", "1657", "1759", "1867", "2011" ]
[ "nonn", "easy" ]
108
1
1
[ "A000040", "A000384", "A001358", "A005382", "A005383", "A005384", "A005603", "A006254", "A010051", "A023204", "A053685", "A057326", "A057327", "A057328", "A057329", "A057330", "A063908", "A063909" ]
[ "M0849" ]
N. J. A. Sloane
2024-12-17T08:32:11
oeisdata/seq/A005/A005382.seq
5ae808ba3145cc7a44833f8e83805746
A005383
Primes p such that (p+1)/2 is prime.
[ "3", "5", "13", "37", "61", "73", "157", "193", "277", "313", "397", "421", "457", "541", "613", "661", "673", "733", "757", "877", "997", "1093", "1153", "1201", "1213", "1237", "1321", "1381", "1453", "1621", "1657", "1753", "1873", "1933", "1993", "2017", "2137", "2341", "2473", "2557", "2593", "2797", "2857", "2917", "3061", "3217", "3253" ]
[ "nonn", "easy" ]
136
1
1
[ "A000040", "A005382", "A005383", "A005385", "A005603", "A010051", "A036570", "A048161", "A057326", "A057327", "A057328", "A057329", "A057330", "A065091" ]
[ "M2492" ]
N. J. A. Sloane
2022-09-08T08:44:33
oeisdata/seq/A005/A005383.seq
9646d703fd91d8a2f8e95d58a1b23aa0
A005384
Sophie Germain primes p: 2p+1 is also prime.
[ "2", "3", "5", "11", "23", "29", "41", "53", "83", "89", "113", "131", "173", "179", "191", "233", "239", "251", "281", "293", "359", "419", "431", "443", "491", "509", "593", "641", "653", "659", "683", "719", "743", "761", "809", "911", "953", "1013", "1019", "1031", "1049", "1103", "1223", "1229", "1289", "1409", "1439", "1451", "1481", "1499", "1511", "1559" ]
[ "nonn", "nice", "changed" ]
341
1
1
[ "A000355", "A005384", "A005385", "A005602", "A007528", "A007700", "A023212", "A023272", "A023302", "A023330", "A057331", "A087634", "A092816", "A138025", "A138030", "A156541", "A156542", "A156592", "A156660", "A156874", "A161896", "A278932" ]
[ "M0731" ]
N. J. A. Sloane
2025-04-22T10:47:52
oeisdata/seq/A005/A005384.seq
46556c650fc0409da6c7bec5fed63fdd
A005385
Safe primes p: (p-1)/2 is also prime.
[ "5", "7", "11", "23", "47", "59", "83", "107", "167", "179", "227", "263", "347", "359", "383", "467", "479", "503", "563", "587", "719", "839", "863", "887", "983", "1019", "1187", "1283", "1307", "1319", "1367", "1439", "1487", "1523", "1619", "1823", "1907", "2027", "2039", "2063", "2099", "2207", "2447", "2459", "2579", "2819", "2879", "2903", "2963" ]
[ "nonn", "easy", "nice" ]
195
1
1
[ "A005383", "A005384", "A005385", "A005602", "A007700", "A023272", "A023302", "A023330", "A057331", "A072055", "A079148", "A088707", "A207409", "A263880" ]
[ "M3761" ]
N. J. A. Sloane
2024-12-18T15:05:24
oeisdata/seq/A005/A005385.seq
9b0448a9b80349b6680d1945fae0285f
A005386
Area of n-th triple of squares around a triangle.
[ "1", "3", "16", "75", "361", "1728", "8281", "39675", "190096", "910803", "4363921", "20908800", "100180081", "479991603", "2299777936", "11018898075", "52794712441", "252954664128", "1211978608201", "5806938376875", "27822713276176", "133306628004003", "638710426743841", "3060245505715200" ]
[ "nonn", "easy" ]
61
1
2
[ "A003769", "A005386", "A099025", "A100047" ]
[ "M3017" ]
Jean Meeus
2022-11-17T07:20:52
oeisdata/seq/A005/A005386.seq
2b46601cf64718484a0415d3344f10d8
A005387
Number of partitional matroids on n elements.
[ "1", "2", "5", "16", "62", "276", "1377", "7596", "45789", "298626", "2090910", "15621640", "123897413", "1038535174", "9165475893", "84886111212", "822648571314", "8321077557124", "87648445601429", "959450073912136", "10894692556576613", "128114221270929646" ]
[ "nonn", "easy", "nice" ]
33
0
2
[ "A005387", "A327006" ]
[ "M1493" ]
N. J. A. Sloane
2022-11-17T07:20:47
oeisdata/seq/A005/A005387.seq
f9d1f7c374e81943072bd1e2094ceb3b
A005388
Number of degree-n permutations of order a power of 2.
[ "1", "1", "2", "4", "16", "56", "256", "1072", "11264", "78976", "672256", "4653056", "49810432", "433429504", "4448608256", "39221579776", "1914926104576", "29475151020032", "501759779405824", "6238907914387456", "120652091860975616", "1751735807564578816", "29062253310781161472", "398033706586943258624" ]
[ "nonn", "nice", "easy" ]
45
0
3
[ "A000085", "A001470", "A001472", "A005388", "A053495", "A053496", "A053497", "A053498", "A053499", "A053500", "A053501", "A053502", "A053503", "A053504", "A053505" ]
[ "M1293" ]
N. J. A. Sloane and J. H. Conway
2024-07-06T14:03:35
oeisdata/seq/A005/A005388.seq
0578cbbc4eb793f79b64f9dc1721c2e3
A005389
Number of Hamiltonian circuits on 2n times 4 rectangle.
[ "1", "6", "37", "236", "1517", "9770", "62953", "405688", "2614457", "16849006", "108584525", "699780452", "4509783909", "29063617746", "187302518353", "1207084188912", "7779138543857", "50133202843990", "323086934794997", "2082156365731164", "13418602439355485", "86477122654688250", "557307869909156153" ]
[ "nonn", "easy" ]
51
1
2
[ "A005389", "A006864" ]
[ "M4228" ]
N. J. A. Sloane, Simon Plouffe
2022-11-18T03:40:59
oeisdata/seq/A005/A005389.seq
e3a1ec724e9d5f7f7afc1e81face3a7a
A005390
Number of Hamiltonian circuits on 2n X 6 rectangle.
[ "1", "37", "1072", "32675", "1024028", "32463802", "1033917350", "32989068162", "1053349394128", "33643541208290", "1074685815276400", "34330607094625734", "1096704136430950646", "35034883701169366742", "1119214052513009716324", "35754123580486507079548" ]
[ "nonn" ]
23
1
2
[ "A005390", "A145401" ]
[ "M5264" ]
N. J. A. Sloane
2022-11-18T03:42:12
oeisdata/seq/A005/A005390.seq
cbe45a0da55e2a9f926b3c5be3fdaf52
A005391
Number of Hamiltonian circuits on 2n X 8 rectangle.
[ "1", "236", "32675", "4638576", "681728204", "102283239429", "15513067188008", "2365714170297014", "361749878496079778", "55391169255983979555", "8487168277379774266411", "1300854247070195164448395", "199418506963731877069653608", "30572953033472980838613625389" ]
[ "nonn" ]
20
1
2
null
[ "M5415" ]
N. J. A. Sloane.
2025-02-16T08:32:28
oeisdata/seq/A005/A005391.seq
6dd80da17d7fb46e86bcf824e613ccbd
A005392
Coefficients of high-temperature series for specific heat of spin-1/2 Ising model on a cristobalite lattice.
[ "3", "12", "15", "-36", "-138", "276", "4326", "21204", "65274", "126204", "204246", "1267356", "10235538", "54791316", "212311746", "678889380", "4946455134", "20113372464" ]
[ "sign", "nice" ]
15
0
1
null
[ "M2915" ]
N. J. A. Sloane
2022-01-31T01:38:34
oeisdata/seq/A005/A005392.seq
34947e89972d97a5fa2575da87cad5df
A005393
Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded down.
[ "0", "0", "1", "5", "23", "118", "710", "4980", "39902", "359536", "3598695", "39615625", "475687486", "6187239475", "86661001740", "1300430722199", "20814114415223", "353948328666100", "6372804626194309", "121112786592293963", "2422786846761133393", "50888617325509644403" ]
[ "nonn", "easy" ]
16
0
4
[ "A005393", "A005395" ]
null
N. J. A. Sloane
2022-09-08T08:44:33
oeisdata/seq/A005/A005393.seq
3bde313ece7618b76315e95606bdeab3
A005394
Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded to nearest integer.
[ "0", "1", "2", "6", "24", "118", "710", "4980", "39902", "359537", "3598696", "39615625", "475687486", "6187239475", "86661001741", "1300430722199", "20814114415223", "353948328666101", "6372804626194309", "121112786592293963", "2422786846761133394", "50888617325509644403", "1119751494628234263302" ]
[ "nonn" ]
13
0
3
[ "A000142", "A005394", "A090583" ]
null
N. J. A. Sloane
2024-01-24T09:43:41
oeisdata/seq/A005/A005394.seq
f9f8bb008255556dc2088e854caa8185
A005395
Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded up.
[ "0", "1", "2", "6", "24", "119", "711", "4981", "39903", "359537", "3598696", "39615626", "475687487", "6187239476", "86661001741", "1300430722200", "20814114415224", "353948328666101", "6372804626194310", "121112786592293964", "2422786846761133394", "50888617325509644404", "1119751494628234263303" ]
[ "nonn", "easy" ]
13
0
3
[ "A005393", "A005395" ]
null
N. J. A. Sloane
2016-06-12T02:47:48
oeisdata/seq/A005/A005395.seq
1a3ffea29f30c48e62c5be25fd5e29df
A005396
Number of 2n-step polygons on honeycomb.
[ "1", "0", "0", "6", "0", "30", "24", "168", "288", "1170", "2760", "9504", "25776", "84006", "244104", "779970", "2356800", "7487310", "23167656", "73639326", "231348000", "737718534", "2341772136", "7498417956", "23982456384", "77119604400", "248088123192", "800978437674", "2588744704560", "8388692108016", "27217694697000" ]
[ "nonn" ]
21
2
4
[ "A001335", "A005396" ]
[ "M4043" ]
N. J. A. Sloane.
2020-08-07T02:11:20
oeisdata/seq/A005/A005396.seq
b5a93f64f76ae92cc9ccc4cd18d30444
A005397
Number of n-step polygons on Kagome lattice.
[ "4", "0", "0", "4", "28", "80", "120", "120", "264", "1080", "3120", "6440", "11960", "26688", "70448", "179340", "415796", "935560", "2195536", "5374468", "13145420", "31504224", "74955600", "180228984", "438624648", "1069909344", "2600077824", "6310088640", "15363918432" ]
[ "nonn" ]
16
3
1
[ "A001665", "A005397" ]
[ "M3186" ]
N. J. A. Sloane.
2020-08-15T19:55:27
oeisdata/seq/A005/A005397.seq
09f7e609f8c2dcdc3cf1ef11c7f99bd2
A005398
Number of n-step polygons on f.c.c. lattice.
[ "8", "33", "168", "970", "6168", "42069", "301376", "2241420", "17173224", "134806948", "1079802216", "8798329080", "72748583832", "609220407150", "5158999447488" ]
[ "nonn", "more", "nice" ]
34
3
1
[ "A001337", "A005398" ]
[ "M4512" ]
N. J. A. Sloane
2024-04-05T19:46:30
oeisdata/seq/A005/A005398.seq
3424dc26a97b3ee06f5b16e565fb6568
A005399
E.g.f.: high-temperature series in J/2kT for ferromagnetic susceptibility for the spin-1/2 Heisenberg model on hexagonal lattice.
[ "1", "6", "48", "408", "3600", "42336", "781728", "13646016", "90893568", "-1798204416", "70794720768", "7538546211840", "63813109782528", "-12977417912045568", "-320549902414196736", "33016479733605777408", "1709506241695601983488" ]
[ "sign", "more" ]
33
0
2
[ "A002920", "A005399", "A005400", "A005401", "A005402", "A047709" ]
[ "M4256" ]
N. J. A. Sloane
2024-11-25T12:16:18
oeisdata/seq/A005/A005399.seq
a83a1c381409588cc5e9c4c746591a8d
A005400
High temperature series for spin-1/2 Heisenberg specific heat on 2D hexagonal lattice.
[ "0", "9", "18", "-306", "-3240", "49176", "1466640", "-13626000", "-1172668032", "75256704", "1392243773184", "18426692664576", "-2213592367094784", "-74200148173310976", "4271973657228822528", "294089252618987845632", "-8526609981314268364800", "-1299100041545138822873088" ]
[ "sign" ]
39
1
2
[ "A005399", "A005400", "A005402" ]
[ "M4603" ]
N. J. A. Sloane
2024-11-25T12:16:04
oeisdata/seq/A005/A005400.seq
5c5be189526f5149fe50230b220fc0fd