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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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32
A008301
Poupard's triangle: triangle of numbers arising in enumeration of binary trees.
[ "1", "1", "2", "1", "4", "8", "10", "8", "4", "34", "68", "94", "104", "94", "68", "34", "496", "992", "1420", "1712", "1816", "1712", "1420", "992", "496", "11056", "22112", "32176", "40256", "45496", "47312", "45496", "40256", "32176", "22112", "11056", "349504", "699008", "1026400", "1309568", "1528384", "1666688", "1714000" ]
[ "nonn", "tabf", "easy", "nice" ]
63
0
3
[ "A002105", "A008301", "A107652", "A210108" ]
null
N. J. A. Sloane
2019-12-14T08:23:02
oeisdata/seq/A008/A008301.seq
651b0f86a5c64067d92b1af810015bb2
A008302
Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_{i=0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index.
[ "1", "1", "1", "1", "2", "2", "1", "1", "3", "5", "6", "5", "3", "1", "1", "4", "9", "15", "20", "22", "20", "15", "9", "4", "1", "1", "5", "14", "29", "49", "71", "90", "101", "101", "90", "71", "49", "29", "14", "5", "1", "1", "6", "20", "49", "98", "169", "259", "359", "455", "531", "573", "573", "531", "455", "359", "259", "169", "98", "49", "20", "6", "1", "1", "7", "27", "76", "174", "343", "602", "961", "1415", "1940", "2493", "3017", "3450", "3736", "3836", "3736", "3450", "3017", "2493", "1940", "1415", "961", "602", "343", "174", "76", "27", "7", "1", "1", "8", "35", "111", "285", "628", "1230", "2191", "3606", "5545", "8031", "11021", "14395", "17957", "21450", "24584", "27073", "28675", "29228", "28675", "27073", "24584", "21450", "17957", "14395", "11021", "8031", "5545", "3606", "2191", "1230", "628", "285", "111", "35", "8", "1" ]
[ "easy", "tabf", "nonn", "nice", "look", "changed" ]
403
1
5
[ "A000124", "A000140", "A000142", "A000217", "A000707", "A001809", "A001892", "A001893", "A001894", "A005283", "A005284", "A005285", "A005286", "A005287", "A005288", "A008302", "A060701", "A069777", "A139365", "A161435", "A161436", "A161437", "A161438", "A161439", "A161456", "A161457", "A242656", "A242657", "A357611" ]
null
N. J. A. Sloane
2025-04-21T09:38:49
oeisdata/seq/A008/A008302.seq
d3f790f94597748f97241083def3040e
A008303
Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks.
[ "1", "2", "4", "2", "8", "16", "16", "88", "16", "32", "416", "272", "64", "1824", "2880", "272", "128", "7680", "24576", "7936", "256", "31616", "185856", "137216", "7936", "512", "128512", "1304832", "1841152", "353792", "1024", "518656", "8728576", "21253376", "9061376", "353792", "2048", "2084864", "56520704", "222398464", "175627264", "22368256" ]
[ "nonn", "tabf" ]
233
1
2
[ "A000079", "A000111", "A000142", "A000182", "A000431", "A000487", "A000517", "A008303", "A011782", "A090672", "A101280", "A179708", "A179709", "A179710", "A185896", "A242783", "A242784" ]
null
N. J. A. Sloane
2024-10-26T10:47:41
oeisdata/seq/A008/A008303.seq
a65d4f94bd35bdb5a9d4fb82312dce9e
A008304
Triangle read by rows: T(n,k) (n>=1; 1<=k<=n) is the number of permutations of [n] in which the longest increasing run has length k.
[ "1", "1", "1", "1", "4", "1", "1", "16", "6", "1", "1", "69", "41", "8", "1", "1", "348", "293", "67", "10", "1", "1", "2016", "2309", "602", "99", "12", "1", "1", "13357", "19975", "5811", "1024", "137", "14", "1", "1", "99376", "189524", "60875", "11304", "1602", "181", "16", "1", "1", "822040", "1960041", "690729", "133669", "19710", "2360", "231", "18", "1", "1", "7477161" ]
[ "nonn", "tabl" ]
71
1
5
[ "A000012", "A000142", "A000303", "A000402", "A000434", "A000456", "A000467", "A008304", "A064314", "A064315", "A230055", "A230234", "A230235", "A230236", "A230251", "A230341", "A230342", "A230343", "A230344", "A230345", "A230346", "A230347", "A230348", "A230349", "A230350" ]
null
N. J. A. Sloane
2023-11-28T13:05:03
oeisdata/seq/A008/A008304.seq
b0e8ee25d166524f3227fa356ba0d617
A008305
Triangle read by rows: a(n,k) = number of permutations of [n] allowing i->i+j (mod n), j=0..k-1.
[ "1", "1", "2", "1", "2", "6", "1", "2", "9", "24", "1", "2", "13", "44", "120", "1", "2", "20", "80", "265", "720", "1", "2", "31", "144", "579", "1854", "5040", "1", "2", "49", "264", "1265", "4738", "14833", "40320", "1", "2", "78", "484", "2783", "12072", "43387", "133496", "362880", "1", "2", "125", "888", "6208", "30818", "126565", "439792", "1334961", "3628800" ]
[ "nonn", "tabl" ]
75
1
3
[ "A000142", "A000166", "A000179", "A000183", "A000211", "A000382", "A000803", "A000804", "A000805", "A002467", "A004306", "A004307", "A008305", "A048162", "A184965", "A189389", "A306714", "A306738" ]
null
N. J. A. Sloane
2019-04-22T01:14:30
oeisdata/seq/A008/A008305.seq
79e25287ab1f826e137d352f22d53842
A008306
Triangle T(n,k) read by rows: associated Stirling numbers of first kind (n >= 2, 1 <= k <= floor(n/2)).
[ "1", "2", "6", "3", "24", "20", "120", "130", "15", "720", "924", "210", "5040", "7308", "2380", "105", "40320", "64224", "26432", "2520", "362880", "623376", "303660", "44100", "945", "3628800", "6636960", "3678840", "705320", "34650", "39916800", "76998240", "47324376", "11098780", "866250", "10395" ]
[ "tabf", "nonn", "nice", "easy" ]
96
2
2
[ "A000142", "A000166", "A000276", "A000483", "A008306", "A079510", "A106828", "A111999", "A235706" ]
null
N. J. A. Sloane
2025-02-16T08:32:32
oeisdata/seq/A008/A008306.seq
8eaabfac7780093182f5c32c3d5090ae
A008307
Table T(n,k) giving number of permutations of [1..n] with order dividing k, read by antidiagonals.
[ "1", "1", "1", "1", "2", "1", "1", "4", "1", "1", "1", "10", "3", "2", "1", "1", "26", "9", "4", "1", "1", "1", "76", "21", "16", "1", "2", "1", "1", "232", "81", "56", "1", "6", "1", "1", "1", "764", "351", "256", "25", "18", "1", "2", "1", "1", "2620", "1233", "1072", "145", "66", "1", "4", "1", "1", "1", "9496", "5769", "6224", "505", "396", "1", "16", "3", "2", "1", "1", "35696", "31041", "33616", "1345", "2052", "1", "56", "9", "4", "1", "1" ]
[ "nonn", "tabl", "easy", "look", "nice" ]
48
1
5
[ "A000012", "A000034", "A000085", "A001470", "A001472", "A008307", "A052501", "A053496", "A053497", "A053498", "A053499", "A053500", "A053501", "A053502", "A053503", "A053504", "A053505", "A074759", "A284517", "A284518" ]
null
N. J. A. Sloane
2021-12-16T22:19:48
oeisdata/seq/A008/A008307.seq
7a09679ecb4b8c8c4a0ed5ee2012bf35
A008308
Triangle of tangent numbers.
[ "1", "1", "2", "1", "8", "1", "16", "20", "1", "136", "40", "1", "272", "616", "70", "1", "3968", "2016", "112", "1", "7936", "28160", "5376", "168", "1", "176896", "135680", "12432", "240", "1", "353792", "1805056", "508640", "25872", "330", "1", "11184128", "11977856", "1595264", "49632", "440", "1", "22368256", "154918400", "59835776" ]
[ "tabf", "nonn", "nice" ]
15
1
3
[ "A006229", "A008308", "A059419" ]
null
N. J. A. Sloane
2021-12-17T05:38:47
oeisdata/seq/A008/A008308.seq
60256f90c322130a2a5632aeebdf4292
A008309
Triangle T(n,k) of arctangent numbers: expansion of arctan(x)^n/n!.
[ "1", "1", "-2", "1", "-8", "1", "24", "-20", "1", "184", "-40", "1", "-720", "784", "-70", "1", "-8448", "2464", "-112", "1", "40320", "-52352", "6384", "-168", "1", "648576", "-229760", "14448", "-240", "1", "-3628800", "5360256", "-804320", "29568", "-330", "1" ]
[ "sign", "tabf", "nice" ]
28
1
3
[ "A007290", "A008309", "A010050", "A049034", "A049214", "A049215", "A049216", "A049217", "A049218" ]
null
N. J. A. Sloane
2017-10-07T03:40:32
oeisdata/seq/A008/A008309.seq
a46c9a5d6c6217f05b19251d30327bfc
A008310
Triangle of coefficients of Chebyshev polynomials T_n(x).
[ "1", "1", "-1", "2", "-3", "4", "1", "-8", "8", "5", "-20", "16", "-1", "18", "-48", "32", "-7", "56", "-112", "64", "1", "-32", "160", "-256", "128", "9", "-120", "432", "-576", "256", "-1", "50", "-400", "1120", "-1280", "512", "-11", "220", "-1232", "2816", "-2816", "1024", "1", "-72", "840", "-3584", "6912", "-6144", "2048", "13", "-364", "2912", "-9984", "16640", "-13312", "4096" ]
[ "sign", "tabf", "nice", "easy" ]
140
0
4
[ "A001075", "A001079", "A001081", "A001085", "A001091", "A001541", "A001792", "A001793", "A001794", "A006974", "A006975", "A006976", "A008310", "A008312", "A011782", "A011943", "A023038", "A023039", "A028297", "A039991", "A053112", "A053120", "A068203", "A077422", "A077424", "A097308", "A097310" ]
null
N. J. A. Sloane
2025-04-06T23:59:29
oeisdata/seq/A008/A008310.seq
0c61bc21d1109510ce5f90c470cb3ed7
A008311
Triangle of expansions of powers of x in terms of Chebyshev polynomials T_n (x).
[ "1", "1", "1", "1", "3", "1", "3", "4", "1", "10", "5", "1", "10", "15", "6", "1", "35", "21", "7", "1", "35", "56", "28", "8", "1", "126", "84", "36", "9", "1", "126", "210", "120", "45", "10", "1", "462", "330", "165", "55", "11", "1", "462", "792", "495", "220", "66", "12", "1", "1716", "1287", "715", "286", "78", "13", "1", "1716", "3003", "2002", "1001", "364", "91", "14", "1", "6435", "5005", "3003" ]
[ "nonn", "tabf", "easy" ]
33
0
5
[ "A008311", "A100257" ]
null
N. J. A. Sloane
2018-05-08T15:11:54
oeisdata/seq/A008/A008311.seq
eb75d5a8a54733812f7c914e639beaf0
A008312
Triangle of coefficients of Chebyshev polynomials U_n(x).
[ "1", "2", "-1", "4", "-4", "8", "1", "-12", "16", "6", "-32", "32", "-1", "24", "-80", "64", "-8", "80", "-192", "128", "1", "-40", "240", "-448", "256", "10", "-160", "672", "-1024", "512", "-1", "60", "-560", "1792", "-2304", "1024", "-12", "280", "-1792", "4608", "-5120", "2048" ]
[ "sign", "tabf", "easy", "nice" ]
32
0
2
[ "A008310", "A008312", "A053112", "A053117", "A053118" ]
null
N. J. A. Sloane
2021-12-17T08:12:39
oeisdata/seq/A008/A008312.seq
f7092ad47432f4e15159f469f4d6205e
A008313
Triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
[ "1", "1", "1", "1", "2", "1", "2", "3", "1", "5", "4", "1", "5", "9", "5", "1", "14", "14", "6", "1", "14", "28", "20", "7", "1", "42", "48", "27", "8", "1", "42", "90", "75", "35", "9", "1", "132", "165", "110", "44", "10", "1", "132", "297", "275", "154", "54", "11", "1", "429", "572", "429", "208", "65", "12", "1", "429", "1001", "1001", "637", "273", "77", "13", "1" ]
[ "nonn", "tabf", "nice", "easy" ]
73
0
5
[ "A001405", "A008313", "A039598", "A039599", "A053121" ]
null
N. J. A. Sloane
2025-03-24T10:21:47
oeisdata/seq/A008/A008313.seq
05beda305ad7a8a8c7b5ccaa96a4391e
A008314
Irregular triangle read by rows: one half of the coefficients of the expansion of (2*x)^n in terms of Chebyshev T-polynomials.
[ "1", "1", "1", "1", "1", "3", "1", "4", "3", "1", "5", "10", "1", "6", "15", "10", "1", "7", "21", "35", "1", "8", "28", "56", "35", "1", "9", "36", "84", "126", "1", "10", "45", "120", "210", "126", "1", "11", "55", "165", "330", "462", "1", "12", "66", "220", "495", "792", "462", "1", "13", "78", "286", "715", "1287", "1716", "1", "14", "91", "364", "1001", "2002", "3003", "1716", "1", "15", "105", "455", "1365", "3003", "5005" ]
[ "nonn", "tabf" ]
53
0
6
[ "A007318", "A008311", "A008314", "A122366", "A127673" ]
null
N. J. A. Sloane
2022-08-12T21:15:54
oeisdata/seq/A008/A008314.seq
1b4b58f3666d77af646ac037c8e6b2bf
A008315
Catalan triangle read by rows. Also triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
[ "1", "1", "1", "1", "1", "2", "1", "3", "2", "1", "4", "5", "1", "5", "9", "5", "1", "6", "14", "14", "1", "7", "20", "28", "14", "1", "8", "27", "48", "42", "1", "9", "35", "75", "90", "42", "1", "10", "44", "110", "165", "132", "1", "11", "54", "154", "275", "297", "132", "1", "12", "65", "208", "429", "572", "429", "1", "13", "77", "273", "637", "1001", "1001", "429", "1", "14", "90", "350", "910", "1638", "2002", "1430", "1", "15", "104" ]
[ "nonn", "tabf", "nice", "easy" ]
110
0
6
[ "A000108", "A001405", "A008315", "A008482", "A009766", "A055151", "A056536", "A120730" ]
null
N. J. A. Sloane
2024-08-03T16:39:09
oeisdata/seq/A008/A008315.seq
695d6e08dd1e8a1831141f29cf9cadf1
A008316
Triangle of coefficients of Legendre polynomials P_n (x).
[ "1", "1", "-1", "3", "-3", "5", "3", "-30", "35", "15", "-70", "63", "-5", "105", "-315", "231", "-35", "315", "-693", "429", "35", "-1260", "6930", "-12012", "6435", "315", "-4620", "18018", "-25740", "12155", "-63", "3465", "-30030", "90090", "-109395", "46189", "-693", "15015", "-90090", "218790", "-230945", "88179", "231", "-18018", "225225", "-1021020", "2078505", "-1939938", "676039" ]
[ "sign", "tabf", "easy", "nice" ]
40
0
4
[ "A001790", "A001800", "A001801", "A008316", "A100258", "A121448" ]
null
N. J. A. Sloane
2025-02-16T08:32:32
oeisdata/seq/A008/A008316.seq
e9d8f471abac8672688bb7d233d56548
A008317
Triangle of coefficients of expansions of powers of x in terms of Legendre polynomials P_n(x) over common denominator.
[ "1", "1", "1", "2", "3", "2", "7", "20", "8", "27", "28", "8", "33", "110", "72", "16", "143", "182", "88", "16", "715", "2600", "2160", "832", "128", "3315", "4760", "2992", "960", "128", "4199", "16150", "15504", "7904", "2176", "256", "20349", "31654", "23408", "10080", "2432", "256", "52003", "208012", "220248", "133952", "50048", "10752" ]
[ "nonn", "tabf", "changed" ]
19
0
4
[ "A001790", "A008317" ]
null
N. J. A. Sloane.
2025-04-14T07:25:34
oeisdata/seq/A008/A008317.seq
97f584bc431105449a22b9dcdd508b52
A008318
Smallest number strictly greater than previous one which is the sum of squares of two previous distinct terms (a(1)=1, a(2)=2).
[ "1", "2", "5", "26", "29", "677", "680", "701", "842", "845", "866", "1517", "458330", "458333", "458354", "459005", "459170", "462401", "462404", "462425", "463076", "463241", "491402", "491405", "491426", "492077", "492242", "708965", "708968", "708989", "709640", "709805", "714026", "714029", "714050", "714701" ]
[ "nonn", "easy", "nice" ]
44
1
2
[ "A008318", "A192476" ]
null
R. Muller
2025-02-16T08:32:32
oeisdata/seq/A008/A008318.seq
116f952bf65bcead127a429346d74338
A008319
Smallest number that is sum of squares of distinct earlier terms.
[ "1", "1", "2", "4", "5", "6", "16", "17", "18", "20", "21", "22", "25", "26", "27", "29", "30", "31", "36", "37", "38", "40", "41", "42", "43", "45", "46", "47", "52", "53", "54", "56", "57", "58", "61", "62", "63", "65", "66", "67", "77", "78", "79", "81", "82", "83", "256", "257", "258", "260", "261", "262", "272", "273", "274", "276", "277", "278", "281", "282", "283", "285", "286", "287", "289", "290", "291" ]
[ "nonn", "easy", "nice" ]
26
1
3
null
null
R. Muller
2025-02-16T08:32:32
oeisdata/seq/A008/A008319.seq
c5806aee223fc85669b9fd8fa8b54535
A008320
Smallest number that is not the sum of squares of two distinct earlier terms.
[ "1", "2", "3", "4", "6", "7", "8", "9", "11", "12", "14", "15", "16", "18", "19", "21", "22", "23", "24", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "38", "39", "41", "42", "43", "44", "46", "47", "48", "49", "51", "54", "55", "56", "57", "59", "60", "61", "62", "63", "64", "66", "67", "69", "70", "71", "72", "74", "75", "76", "77", "78", "79", "81", "83", "84", "86", "87", "88", "89", "91", "92", "93", "94" ]
[ "nonn" ]
25
1
2
[ "A008320", "A026468" ]
null
R. Muller
2025-02-16T08:32:32
oeisdata/seq/A008/A008320.seq
6a146c9b70c2ec0083e6eddaf5219d3b
A008321
Smallest number that is not the sum of squares of distinct earlier terms.
[ "1", "2", "3", "6", "7", "8", "11", "12", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "38", "39", "42", "43", "44", "47", "48", "51", "52", "55", "56", "57", "60", "61", "66", "67", "70", "71", "72", "75", "76", "79", "80", "81", "82", "83", "84", "87", "88", "91", "92", "93", "96", "97", "102", "103", "106", "107", "108", "111", "112", "115" ]
[ "nonn" ]
23
1
2
null
null
R. Muller
2025-02-16T08:32:32
oeisdata/seq/A008/A008321.seq
42466c866940e6a07d15dd577e4dfa6f
A008322
Smallest number that is sum of cubes of two distinct earlier terms.
[ "1", "2", "9", "730", "737", "389017001", "389017008", "389017729", "400315554", "400315561", "400316282", "789332553", "58871587162270593034051002", "58871587162270593034051009", "58871587162270593034051730" ]
[ "nonn" ]
16
1
2
null
null
R. Muller
2025-02-16T08:32:32
oeisdata/seq/A008/A008322.seq
bdf649e4464022444962aeada5393d32
A008323
Number of simple connected regular bipartite graphs with 2n nodes.
[ "1", "1", "1", "2", "3", "5", "12", "34", "218", "4278", "431165", "162267174", "201636689352", "777816803938932", "9865957936943859185", "395886667549681686369527", "53716176608076643470380213991", "23524515269630339982914608683548933", "35682168849414944013547274439525153167248" ]
[ "nonn", "hard", "nice" ]
22
0
4
[ "A005142", "A008323", "A008324", "A008326" ]
null
Brendan McKay
2020-04-03T21:45:02
oeisdata/seq/A008/A008323.seq
8acc608dd56eecdd603b4b62c3aa5d30
A008324
Number of simple regular bipartite graphs with 2n nodes.
[ "1", "2", "3", "4", "6", "8", "18", "40", "230", "4296", "431206", "162267272", "201636689771", "777816803942186", "9865957936943931964", "395886667549681689591841", "53716176608076643470621234239", "23524515269630339982914646821899537", "35682168849414944013547274452501768506834" ]
[ "nonn", "hard", "nice" ]
21
0
2
[ "A008323", "A008324", "A008327", "A033995", "A333732" ]
null
Brendan McKay
2020-04-04T11:04:11
oeisdata/seq/A008/A008324.seq
e8eaa5f913464af44c72facd511abf61
A008325
Number of simple regular trivalent bipartite graphs with 2n nodes.
[ "1", "1", "2", "6", "14", "41", "157", "725", "4196", "29816", "246644", "2297075", "23503477", "260265023", "3090336300", "39101547971", "524782945991", "7443247863498", "111221983956652", "1746165682538497", "28734206614035245", "494526496354065244", "8883865784392246280", "166286434745252091055", "3237719048384605059117", "65477287940472122129194" ]
[ "nonn", "hard" ]
28
3
3
[ "A004066", "A006823", "A008325", "A008327" ]
null
Brendan McKay
2020-04-04T11:04:58
oeisdata/seq/A008/A008325.seq
0b97aca40031cf633a747003ea859cea
A008326
Triangle read by rows: T(n,k) is the number of simple regular connected bipartite graphs with 2n nodes and degree k, (2 <= k <= n).
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "5", "4", "1", "1", "1", "13", "14", "4", "1", "1", "1", "38", "129", "41", "7", "1", "1", "1", "149", "1980", "1981", "157", "8", "1", "1", "1", "703", "62611", "304495", "62616", "725", "12", "1", "1", "1", "4132", "2806490", "78322915", "78322916", "2806508", "4196", "14", "1", "1", "1", "29579", "158937213", "27033154060", "147252447227", "27033154065", "158937367", "29817", "21", "1", "1" ]
[ "nonn", "hard", "tabl" ]
26
2
8
[ "A006823", "A006824", "A006825", "A008323", "A008326", "A008327", "A014385", "A014387", "A133687", "A333159" ]
null
Brendan McKay and Eric Rogoyski
2020-04-04T19:18:12
oeisdata/seq/A008/A008326.seq
9e64b6ae03f83ce090f625711344ebe9
A008327
Triangle read by rows: T(n,k) is the number of simple regular bipartite graphs with 2n nodes and degree k, (0 <= k <= n).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "4", "6", "4", "1", "1", "1", "1", "4", "14", "14", "4", "1", "1", "1", "1", "7", "41", "130", "41", "7", "1", "1", "1", "1", "8", "157", "1981", "1981", "157", "8", "1", "1", "1", "1", "12", "725", "62616", "304496", "62616", "725", "12", "1", "1", "1", "1", "14", "4196", "2806508", "78322916" ]
[ "nonn", "tabl", "nice" ]
20
0
13
[ "A000012", "A002865", "A008324", "A008325", "A008326", "A008327", "A051031", "A087114", "A133687", "A333159", "A333730", "A333731" ]
null
Brendan McKay
2020-04-04T14:39:43
oeisdata/seq/A008/A008327.seq
c3b2026fc82e3072d8f3fbb8bff46d2c
A008328
Number of divisors of prime(n)-1.
[ "1", "2", "3", "4", "4", "6", "5", "6", "4", "6", "8", "9", "8", "8", "4", "6", "4", "12", "8", "8", "12", "8", "4", "8", "12", "9", "8", "4", "12", "10", "12", "8", "8", "8", "6", "12", "12", "10", "4", "6", "4", "18", "8", "14", "9", "12", "16", "8", "4", "12", "8", "8", "20", "8", "9", "4", "6", "16", "12", "16", "8", "6", "12", "8", "16", "6", "16", "20", "4", "12", "12", "4", "8", "12", "16", "4", "6", "18", "15", "16", "8", "24", "8" ]
[ "nonn", "easy" ]
43
1
2
[ "A000005", "A006093", "A008328", "A066800", "A103199" ]
null
N. J. A. Sloane
2025-04-03T08:59:36
oeisdata/seq/A008/A008328.seq
6d809454eeaedbd90187dc4003941b3e
A008329
Number of divisors of p+1, p prime.
[ "2", "3", "4", "4", "6", "4", "6", "6", "8", "8", "6", "4", "8", "6", "10", "8", "12", "4", "6", "12", "4", "10", "12", "12", "6", "8", "8", "12", "8", "8", "8", "12", "8", "12", "12", "8", "4", "6", "16", "8", "18", "8", "14", "4", "12", "12", "6", "12", "12", "8", "12", "20", "6", "18", "8", "16", "16", "10", "4", "8", "6", "12", "12", "16", "4", "8", "6", "6", "12", "12", "8", "24", "10", "8", "12", "16", "16", "4", "8", "8", "24", "4", "20", "8", "16" ]
[ "nonn" ]
28
1
1
[ "A000005", "A008329", "A008864" ]
null
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A008/A008329.seq
a883387ed8b42e3ecf2033e4df3fc5df
A008330
phi(p-1), as p runs through the primes.
[ "1", "1", "2", "2", "4", "4", "8", "6", "10", "12", "8", "12", "16", "12", "22", "24", "28", "16", "20", "24", "24", "24", "40", "40", "32", "40", "32", "52", "36", "48", "36", "48", "64", "44", "72", "40", "48", "54", "82", "84", "88", "48", "72", "64", "84", "60", "48", "72", "112", "72", "112", "96", "64", "100", "128", "130", "132", "72", "88", "96", "92", "144", "96", "120", "96", "156", "80", "96", "172", "112" ]
[ "nonn", "look" ]
52
1
3
[ "A000010", "A008330", "A241194", "A241195", "A338364" ]
null
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A008/A008330.seq
5bf87c7c6d4120a9c4a91b438790b066
A008331
a(n) = phi(prime(n)+1).
[ "2", "2", "2", "4", "4", "6", "6", "8", "8", "8", "16", "18", "12", "20", "16", "18", "16", "30", "32", "24", "36", "32", "24", "24", "42", "32", "48", "36", "40", "36", "64", "40", "44", "48", "40", "72", "78", "80", "48", "56", "48", "72", "64", "96", "60", "80", "104", "96", "72", "88", "72", "64", "110", "72", "84", "80", "72", "128", "138", "92", "140", "84", "120", "96", "156", "104", "164", "156", "112", "120", "116" ]
[ "nonn" ]
18
1
1
[ "A000010", "A008331", "A008864", "A363700" ]
null
N. J. A. Sloane
2023-06-20T10:02:49
oeisdata/seq/A008/A008331.seq
03c53bab2dee45be7f2941ea65115237
A008332
Sum of divisors of p-1, p prime.
[ "1", "3", "7", "12", "18", "28", "31", "39", "36", "56", "72", "91", "90", "96", "72", "98", "90", "168", "144", "144", "195", "168", "126", "180", "252", "217", "216", "162", "280", "248", "312", "252", "270", "288", "266", "372", "392", "363", "252", "308", "270", "546", "360", "508", "399", "468", "576", "456", "342", "560", "450", "432", "744", "468", "511", "396", "476", "720", "672" ]
[ "nonn", "easy" ]
35
1
2
[ "A000203", "A006093", "A008332", "A082695" ]
null
N. J. A. Sloane.
2022-09-08T08:44:35
oeisdata/seq/A008/A008332.seq
74d3c188dd8b438d4288c81a21568009
A008333
Sum of divisors of p+1, p prime.
[ "4", "7", "12", "15", "28", "24", "39", "42", "60", "72", "63", "60", "96", "84", "124", "120", "168", "96", "126", "195", "114", "186", "224", "234", "171", "216", "210", "280", "216", "240", "255", "336", "288", "336", "372", "300", "240", "294", "480", "360", "546", "336", "508", "294", "468", "465", "378", "504", "560", "432", "546", "744", "399", "728", "528", "720", "720", "558" ]
[ "nonn", "easy" ]
28
1
1
[ "A000203", "A008333", "A008864", "A051027" ]
null
N. J. A. Sloane
2020-04-19T07:52:35
oeisdata/seq/A008/A008333.seq
0d2f52c7ab5da77aca81fe0027d5eb4e
A008334
Number of distinct primes dividing p-1, where p = n-th prime.
[ "0", "1", "1", "2", "2", "2", "1", "2", "2", "2", "3", "2", "2", "3", "2", "2", "2", "3", "3", "3", "2", "3", "2", "2", "2", "2", "3", "2", "2", "2", "3", "3", "2", "3", "2", "3", "3", "2", "2", "2", "2", "3", "3", "2", "2", "3", "4", "3", "2", "3", "2", "3", "3", "2", "1", "2", "2", "3", "3", "3", "3", "2", "3", "3", "3", "2", "4", "3", "2", "3", "2", "2", "3", "3", "3", "2", "2", "3", "2", "3", "3", "4", "3", "2", "3", "3", "2", "3", "3", "4", "2", "2", "2", "3", "3" ]
[ "nonn" ]
23
1
4
[ "A001221", "A001222", "A006093", "A008334", "A023508" ]
null
N. J. A. Sloane.
2024-11-30T07:00:10
oeisdata/seq/A008/A008334.seq
3abd4f453e3a5213b3f30efa86411337
A008335
Number of distinct primes dividing p+1 as p runs through the primes.
[ "1", "1", "2", "1", "2", "2", "2", "2", "2", "3", "1", "2", "3", "2", "2", "2", "3", "2", "2", "2", "2", "2", "3", "3", "2", "3", "2", "2", "3", "3", "1", "3", "3", "3", "3", "2", "2", "2", "3", "3", "3", "3", "2", "2", "3", "2", "2", "2", "3", "3", "3", "3", "2", "3", "3", "3", "3", "2", "2", "3", "2", "3", "3", "3", "2", "3", "2", "2", "3", "3", "3", "3", "2", "3", "3", "2", "4", "2", "3", "3", "4", "2", "2", "3", "3", "3", "3", "2", "4", "2", "3", "3", "2", "3", "2" ]
[ "nonn", "easy" ]
15
1
3
[ "A001221", "A008335", "A008864", "A023514" ]
null
N. J. A. Sloane.
2024-09-10T08:44:39
oeisdata/seq/A008/A008335.seq
030a08a0d0ae6b0b95f8bf6a92f6d776
A008336
a(n+1) = a(n)/n if n|a(n) else a(n)*n, a(1) = 1.
[ "1", "1", "2", "6", "24", "120", "20", "140", "1120", "10080", "1008", "11088", "924", "12012", "858", "12870", "205920", "3500640", "194480", "3695120", "184756", "3879876", "176358", "4056234", "97349616", "2433740400", "93605400", "2527345800", "90262350", "2617608150", "87253605", "2704861755", "86555576160", "2856334013280" ]
[ "nonn", "easy", "nice", "look" ]
81
1
3
[ "A005132", "A008336", "A065422", "A195504", "A260850", "A337486", "A370968" ]
null
Bernardo Recamán
2024-04-15T13:10:29
oeisdata/seq/A008/A008336.seq
99e4a2dceff4f6ec6c8a26529faccf58
A008337
Number of orbits on points that are at n steps from 0 in E_8 lattice.
[ "1", "1", "3", "5", "10", "15", "27", "40", "63", "91", "134", "188", "265" ]
[ "nonn", "hard" ]
14
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008337.seq
0e1a84687e214fd231dd8c1a81e7fca9
A008338
a(n+1) = a(n)/n! if n! divides a(n) else a(n)*n!.
[ "1", "1", "2", "12", "288", "34560", "48", "241920", "6", "2177280", "7900913664000", "315379190543155200000", "658409472000", "4099929477061017600000", "47029248000", "61498942155915264000000", "2939328000", "1045482016650559488000000", "163296000" ]
[ "nonn", "easy", "nice" ]
17
1
3
null
null
N. J. A. Sloane
2018-07-11T04:33:21
oeisdata/seq/A008/A008338.seq
abcad5694741da143588fa68b154de69
A008339
a(1)=1; for n >= 1, a(n+1) = lcm(a(n),n) / gcd(a(n),n).
[ "1", "1", "2", "6", "6", "30", "5", "35", "280", "2520", "252", "2772", "231", "3003", "858", "1430", "5720", "97240", "437580", "8314020", "415701", "969969", "176358", "4056234", "2704156", "67603900", "2600150", "70204050", "10029150", "290845350", "9694845", "300540195", "9617286240", "35263382880", "1037158320" ]
[ "nonn" ]
28
1
3
[ "A008339", "A249831" ]
null
N. J. A. Sloane.
2015-09-09T19:48:59
oeisdata/seq/A008/A008339.seq
a34ca590f30cce359c520184079783ca
A008340
Coordination sequence for E_8 lattice.
[ "1", "240", "9120", "121680", "864960", "4113840", "14905440", "44480400", "114879360", "265422960", "561403680", "1105317840", "2050966080", "3620750640", "6126497760", "9994133520", "15792541440", "24266930160", "36377039520", "53340513360", "76681767360" ]
[ "nonn", "easy", "nice" ]
35
0
2
[ "A008340", "A008397", "A008399", "A019557", "A019558" ]
null
N. J. A. Sloane and J. H. Conway
2023-12-10T16:02:58
oeisdata/seq/A008/A008340.seq
97df23a616449e1c0c7b95b5cb9db5c9
A008341
a(n)=1, a(n+1) = lcm(a(n),b(n)) / gcd(a(n),b(n)), where {b(n)} = {fibonacci(n)}.
[ "1", "1", "1", "2", "6", "30", "60", "780", "1820", "15470", "34034", "3029026", "109044936", "25407470088", "56678202504", "8643425881860", "19344810307020", "30893662060310940", "17264105268997290", "72181224129677669490" ]
[ "nonn" ]
13
1
4
null
null
N. J. A. Sloane.
2014-01-27T09:12:42
oeisdata/seq/A008/A008341.seq
8f93ff55b9dbd251060751859e448e94
A008342
Minimal number of shift, add and subtract operations to multiply by n.
[ "0", "1", "2", "1", "2", "3", "2", "1", "2", "3", "4", "3", "4", "3", "2", "1", "2", "3", "4", "3", "4", "4", "4", "3", "4", "4", "4", "3", "4", "3", "2", "1", "2", "3", "4", "3", "4", "5", "4", "3", "4", "5", "5", "4", "4", "4", "4", "3", "4", "4", "4", "4", "5", "5", "4", "3", "4", "5", "4", "3", "4", "3", "2", "1", "2", "3", "4", "3", "4", "5", "4", "3", "4", "5", "4", "4", "5", "5", "4", "3", "4", "5", "5", "4", "4", "5", "6", "5", "5", "5", "5", "4", "4", "4", "4", "3", "4", "4", "4" ]
[ "nonn", "nice" ]
14
1
3
null
null
dg(AT)franklin.com (Doug Grundman)
2018-04-15T21:49:42
oeisdata/seq/A008/A008342.seq
7c1999f6c74cdf0d37b73a939b76ad8e
A008343
a(1)=1; thereafter a(n+1) = a(n)-n if a(n) >= n otherwise a(n+1) = a(n)+n.
[ "1", "0", "2", "5", "1", "6", "0", "7", "15", "6", "16", "5", "17", "4", "18", "3", "19", "2", "20", "1", "21", "0", "22", "45", "21", "46", "20", "47", "19", "48", "18", "49", "17", "50", "16", "51", "15", "52", "14", "53", "13", "54", "12", "55", "11", "56", "10", "57", "9", "58", "8", "59", "7", "60", "6", "61", "5", "62", "4", "63", "3" ]
[ "nonn" ]
24
1
3
[ "A008343", "A008344", "A060816" ]
null
N. J. A. Sloane and J. H. Conway
2021-07-09T08:24:23
oeisdata/seq/A008/A008343.seq
c16a8f84c038ae726650cece373c4634
A008344
a(1)=0; thereafter a(n+1) = a(n) - n if a(n) >= n otherwise a(n+1) = a(n) + n.
[ "0", "1", "3", "0", "4", "9", "3", "10", "2", "11", "1", "12", "0", "13", "27", "12", "28", "11", "29", "10", "30", "9", "31", "8", "32", "7", "33", "6", "34", "5", "35", "4", "36", "3", "37", "2", "38", "1", "39", "0", "40", "81", "39", "82", "38", "83", "37", "84", "36", "85", "35", "86", "34", "87", "33", "88", "32", "89", "31", "90", "30", "91", "29", "92", "28", "93", "27", "94", "26", "95", "25", "96", "24", "97", "23", "98" ]
[ "nonn", "easy", "nice", "look" ]
96
1
3
[ "A008343", "A008344", "A046901", "A076042", "A085059", "A086283", "A088230" ]
null
N. J. A. Sloane
2023-10-18T02:11:15
oeisdata/seq/A008/A008344.seq
dfa10823d72dbee73bc0795b7a25ecf9
A008345
a(n+1) = a(n)-b(n+1) if a(n) >= b(n+1) else a(n)+b(n+1), where {b(n)} are the triangular numbers A000217.
[ "0", "1", "4", "10", "0", "15", "36", "8", "44", "89", "34", "100", "22", "113", "8", "128", "264", "111", "282", "92", "302", "71", "324", "48", "348", "23", "374", "752", "346", "781", "316", "812", "284", "845", "250", "880", "214", "917", "176", "956", "136", "997", "94", "1040", "50", "1085", "4", "1132", "2308", "1083", "2358", "1032", "2410", "979", "2464", "924" ]
[ "nonn", "easy" ]
26
0
3
[ "A000217", "A008344", "A008345", "A076042" ]
null
N. J. A. Sloane and J. H. Conway
2020-01-11T07:46:47
oeisdata/seq/A008/A008345.seq
265328a2241e59c2950b9ae2a617099f
A008346
a(n) = Fibonacci(n) + (-1)^n.
[ "1", "0", "2", "1", "4", "4", "9", "12", "22", "33", "56", "88", "145", "232", "378", "609", "988", "1596", "2585", "4180", "6766", "10945", "17712", "28656", "46369", "75024", "121394", "196417", "317812", "514228", "832041", "1346268", "2178310", "3524577", "5702888", "9227464", "14930353", "24157816", "39088170", "63245985", "102334156" ]
[ "nonn", "easy" ]
142
0
3
[ "A007492", "A008346", "A014565", "A066983", "A078024", "A098600", "A099925", "A119282", "A374297" ]
null
N. J. A. Sloane
2024-11-17T19:13:06
oeisdata/seq/A008/A008346.seq
9151f7b138940b74210933f6f01fbd1b
A008347
a(n) = Sum_{i=0..n-1} (-1)^i * prime(n-i).
[ "0", "2", "1", "4", "3", "8", "5", "12", "7", "16", "13", "18", "19", "22", "21", "26", "27", "32", "29", "38", "33", "40", "39", "44", "45", "52", "49", "54", "53", "56", "57", "70", "61", "76", "63", "86", "65", "92", "71", "96", "77", "102", "79", "112", "81", "116", "83", "128", "95", "132", "97", "136", "103", "138", "113", "144", "119", "150", "121", "156", "125", "158", "135", "172", "139", "174", "143" ]
[ "nonn" ]
212
0
2
[ "A000040", "A001223", "A005384", "A007504", "A008347", "A181901", "A226913" ]
null
N. J. A. Sloane and J. H. Conway
2023-11-12T12:57:41
oeisdata/seq/A008/A008347.seq
3de954db4418608d2abbe87a3ca00578
A008348
a(0)=0; thereafter a(n) = a(n-1) + prime(n) if a(n-1) < prime(n), otherwise a(n) = a(n-1) - prime(n).
[ "0", "2", "5", "0", "7", "18", "5", "22", "3", "26", "55", "24", "61", "20", "63", "16", "69", "10", "71", "4", "75", "2", "81", "164", "75", "172", "71", "174", "67", "176", "63", "190", "59", "196", "57", "206", "55", "212", "49", "216", "43", "222", "41", "232", "39", "236", "37", "248", "25", "252", "23", "256", "17", "258", "7", "264", "1", "270", "541", "264", "545", "262", "555" ]
[ "nonn", "look" ]
51
0
2
[ "A008344", "A008348", "A022831", "A022837", "A309225" ]
null
N. J. A. Sloane and J. H. Conway
2024-09-13T15:48:41
oeisdata/seq/A008/A008348.seq
5597468c15d8957cda21cdae09b40ea1
A008349
Crystal ball sequence for E_8 lattice.
[ "1", "241", "9361", "131041", "996001", "5109841", "20015281", "64495681", "179375041", "444798001", "1006201681", "2111519521", "4162485601", "7783236241", "13909734001", "23903867521", "39696408961", "63963339121", "100340378641", "153680892001" ]
[ "nonn", "easy", "nice" ]
39
0
2
null
[ "M5419" ]
N. J. A. Sloane and J. H. Conway
2023-12-10T16:03:59
oeisdata/seq/A008/A008349.seq
97bc9f881b984b7b941d8baba2e7f271
A008350
Number of orbits of norm 2n vectors in E_8 lattice.
[ "1", "1", "1", "1", "2", "1", "1", "2", "2", "2", "2", "2", "2", "3", "2", "2", "4", "3", "3", "4", "3", "3", "4", "4", "3", "5", "4", "5", "6", "5", "3", "6", "6", "5", "6", "6", "6", "8", "6", "6", "7", "7", "6", "10", "8", "7", "8", "9", "7", "10", "9", "9", "11", "11", "8", "11", "10", "10", "12", "12", "9", "13", "11", "13", "14", "13", "10", "17", "14", "12", "13", "15", "13", "17", "15", "15", "17", "18", "13", "19", "16", "16", "18", "21", "15", "20", "18", "19" ]
[ "nonn" ]
27
0
5
null
null
N. J. A. Sloane and J. H. Conway
2021-09-23T02:25:34
oeisdata/seq/A008/A008350.seq
558c2d462bb9d5d985a3da831ee4b207
A008351
a(n) is the concatenation of a(n-1) and a(n-2) with a(1)=1, a(2)=2.
[ "1", "2", "21", "212", "21221", "21221212", "2122121221221", "212212122122121221212", "2122121221221212212122122121221221", "2122121221221212212122122121221221212212122122121221212" ]
[ "nonn", "base" ]
45
1
2
[ "A001950", "A008351", "A008352", "A014675" ]
null
N. J. A. Sloane and J. H. Conway
2024-02-19T01:51:15
oeisdata/seq/A008/A008351.seq
3bce1fb13e9e9759ef64835239eca1c7
A008352
a(n) is formed by concatenating a(n-2) and a(n-1), with a(0) = 1, a(1) = 2.
[ "1", "2", "12", "212", "12212", "21212212", "1221221212212", "212122121221221212212", "1221221212212212122121221221212212", "2121221212212212122121221221212212212122121221221212212" ]
[ "nonn", "base" ]
44
0
2
[ "A000045", "A003849", "A008351", "A008352", "A113773", "A133235" ]
null
N. J. A. Sloane and J. H. Conway
2025-01-18T09:07:41
oeisdata/seq/A008/A008352.seq
9fdfaa2c1f9d2b4854ae84e4888ecda9
A008353
2^n*(2^(n+1) - n - 1).
[ "1", "4", "20", "96", "432", "1856", "7744", "31744", "128768", "519168", "2085888", "8364032", "33501184", "134103040", "536625152", "2146959360", "8588820480", "34357379072", "137433972736", "549745328128", "2199001235456", "8796046884864", "35184275619840", "140737287028736", "562949533990912" ]
[ "nonn", "easy" ]
20
0
2
[ "A008353", "A008464", "A066345" ]
null
N. J. A. Sloane and J. H. Conway
2022-09-08T08:44:35
oeisdata/seq/A008/A008353.seq
541a7ecef174bae8e50c6ea98133e933
A008354
a(n) = (5*n^2 + 1)*n^2 / 6.
[ "0", "1", "14", "69", "216", "525", "1086", "2009", "3424", "5481", "8350", "12221", "17304", "23829", "32046", "42225", "54656", "69649", "87534", "108661", "133400", "162141", "195294", "233289", "276576", "325625", "380926", "442989", "512344", "589541", "675150", "769761", "873984", "988449", "1113806", "1250725", "1399896" ]
[ "nonn", "easy" ]
44
0
3
[ "A005901", "A005902", "A008354" ]
null
N. J. A. Sloane and J. H. Conway
2018-02-12T11:25:59
oeisdata/seq/A008/A008354.seq
b7c899b802421f9ecaad628113994cb9
A008355
Coordination sequence for D_5 lattice.
[ "1", "40", "370", "1640", "4930", "11752", "24050", "44200", "75010", "119720", "182002", "265960", "376130", "517480", "695410", "915752", "1184770", "1509160", "1896050", "2353000", "2888002", "3509480", "4226290", "5047720", "5983490", "7043752" ]
[ "nonn", "easy" ]
32
0
2
[ "A008355", "A103903" ]
null
N. J. A. Sloane and J. H. Conway
2023-12-13T11:02:27
oeisdata/seq/A008/A008355.seq
6cc20f64736ecc9e323dd7c334efe75a
A008356
Crystal ball sequence for D_5 lattice.
[ "1", "41", "411", "2051", "6981", "18733", "42783", "86983", "161993", "281713", "463715", "729675", "1105805", "1623285", "2318695", "3234447", "4419217", "5928377", "7824427", "10177427", "13065429", "16574909", "20801199", "25848919" ]
[ "nonn", "easy" ]
20
0
2
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008356.seq
8f32626972ab1fa53633c422bd1493b0
A008357
Coordination sequence for D_6 lattice.
[ "1", "60", "792", "4724", "18096", "52716", "127816", "271908", "524640", "938652", "1581432", "2537172", "3908624", "5818956", "8413608", "11862148", "16360128", "22130940", "29427672", "38534964", "49770864", "63488684", "80078856" ]
[ "nonn", "easy" ]
29
0
2
[ "A008357", "A103903" ]
null
N. J. A. Sloane and J. H. Conway
2023-12-13T11:05:18
oeisdata/seq/A008/A008357.seq
44f4289e80b5fce8a6e1fffd0540cf73
A008358
Crystal ball sequence for D_6 lattice.
[ "1", "61", "853", "5577", "23673", "76389", "204205", "476113", "1000753", "1939405", "3520837", "6058009", "9966633", "15785589", "24199197", "36061345", "52421473", "74552413", "103980085", "142515049", "192285913", "255774597", "335853453" ]
[ "nonn", "easy" ]
23
0
2
null
null
N. J. A. Sloane and J. H. Conway
2019-07-23T07:59:54
oeisdata/seq/A008/A008358.seq
2893b01753a3c13fd249615d5f4f5f9c
A008359
Coordination sequence for D_7 lattice.
[ "1", "84", "1498", "11620", "55650", "195972", "559258", "1371316", "2999682", "6003956", "11193882", "19695172", "33023074", "53163684", "82663002", "124723732", "183309826", "263258772", "370401626", "511690788", "695335522" ]
[ "nonn", "easy" ]
33
0
2
[ "A008359", "A103903" ]
null
N. J. A. Sloane and J. H. Conway
2019-05-20T03:05:05
oeisdata/seq/A008/A008359.seq
a1985f28c4a327f3390a79f7df8b49e4
A008360
Crystal ball sequence for D_7 lattice.
[ "1", "85", "1583", "13203", "68853", "264825", "824083", "2195399", "5195081", "11199037", "22392919", "42088091", "75111165", "128274849", "210937851", "335661583", "518971409", "782230181", "1152631807", "1664322595", "2359658117", "3290603337", "4520283747" ]
[ "nonn", "easy" ]
55
0
2
null
null
N. J. A. Sloane and J. H. Conway
2022-09-08T08:44:35
oeisdata/seq/A008/A008360.seq
88f288fcf3e10bf4a9711f70503807e5
A008361
Coordination sequence for D_8 lattice.
[ "1", "112", "2592", "25424", "149568", "629808", "2100832", "5910288", "14610560", "32641008", "67232416", "129565392", "236214464", "410909616", "686647008", "1108180624", "1734926592", "2644311920", "3935599392", "5734220368" ]
[ "nonn", "nice", "easy" ]
37
0
2
[ "A008361", "A103903" ]
null
N. J. A. Sloane and J. H. Conway
2023-09-06T01:41:55
oeisdata/seq/A008/A008361.seq
8e6090753e075870058e9f94efa84c2a
A008362
Crystal ball sequence for D_8 lattice.
[ "1", "113", "2705", "28129", "177697", "807505", "2908337", "8818625", "23429185", "56070193", "123302609", "252868001", "489082465", "899992081", "1586639089", "2694819713", "4429746305", "7074058225", "11009657617", "16743877985" ]
[ "nonn", "easy" ]
31
0
2
null
null
N. J. A. Sloane and J. H. Conway
2024-09-20T13:05:25
oeisdata/seq/A008/A008362.seq
4bcec598638f1385c5f073e9642f4055
A008363
a(n) = floor(n/5)*ceiling(n/5).
[ "0", "0", "0", "0", "0", "1", "2", "2", "2", "2", "4", "6", "6", "6", "6", "9", "12", "12", "12", "12", "16", "20", "20", "20", "20", "25", "30", "30", "30", "30", "36", "42", "42", "42", "42", "49", "56", "56", "56", "56", "64", "72", "72", "72", "72", "81", "90", "90", "90", "90", "100", "110", "110", "110", "110", "121", "132", "132" ]
[ "nonn" ]
11
0
7
null
null
N. J. A. Sloane
2016-12-19T01:58:21
oeisdata/seq/A008/A008363.seq
9bf6ae3ec5d913f9b9f4a43576b4198a
A008364
11-rough numbers: not divisible by 2, 3, 5 or 7.
[ "1", "11", "13", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "107", "109", "113", "121", "127", "131", "137", "139", "143", "149", "151", "157", "163", "167", "169", "173", "179", "181", "187", "191", "193", "197", "199", "209", "211", "221", "223", "227", "229", "233", "239", "241", "247" ]
[ "nonn", "easy" ]
132
1
2
[ "A000027", "A002110", "A005408", "A005867", "A007310", "A007775", "A008364", "A008365", "A008366", "A048597", "A049296", "A080672", "A092695", "A166061", "A166063", "A210679" ]
null
N. J. A. Sloane
2025-02-16T08:32:32
oeisdata/seq/A008/A008364.seq
e7e549450e7d14d1925396e74b900641
A008365
13-rough numbers: positive integers that have no prime factors less than 13.
[ "1", "13", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "169", "173", "179", "181", "191", "193", "197", "199", "211", "221", "223", "227", "229", "233", "239", "241", "247", "251", "257", "263", "269" ]
[ "nonn", "easy" ]
73
1
2
[ "A000027", "A005408", "A007310", "A007775", "A008364", "A008365", "A008366", "A166061", "A166063" ]
null
N. J. A. Sloane
2025-02-16T08:32:32
oeisdata/seq/A008/A008365.seq
7ab898c9483b2971ff0731becf0a8ba3
A008366
Smallest prime factor is >= 17.
[ "1", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241", "251", "257", "263", "269", "271", "277", "281", "283" ]
[ "nonn", "easy" ]
55
1
2
[ "A000027", "A005408", "A005867", "A007310", "A007775", "A008364", "A008365", "A008366", "A166061", "A166063" ]
null
N. J. A. Sloane
2025-02-16T08:32:32
oeisdata/seq/A008/A008366.seq
b83cdc8a7bb7935b99c133e45eb91fbc
A008367
Composite but smallest prime factor >= 17.
[ "289", "323", "361", "391", "437", "493", "527", "529", "551", "589", "629", "667", "697", "703", "713", "731", "779", "799", "817", "841", "851", "893", "899", "901", "943", "961", "989", "1003", "1007", "1037", "1073", "1081", "1121", "1139", "1147", "1159", "1189", "1207", "1219", "1241", "1247", "1271", "1273", "1333", "1343", "1349", "1357", "1363", "1369", "1387", "1403", "1411", "1457" ]
[ "nonn" ]
43
1
1
[ "A002808", "A008366", "A008367", "A038511", "A084969", "A084970", "A287391" ]
null
N. J. A. Sloane.
2021-03-22T05:47:06
oeisdata/seq/A008/A008367.seq
aca3004c0bafc02f7d6ec78af2c57a70
A008368
Number of orbits on points that are at n steps from the origin in the f.c.c. lattice.
[ "1", "1", "3", "4", "7", "8", "13", "14", "20", "22", "29", "31", "40" ]
[ "nonn", "more" ]
16
0
3
[ "A008368", "A023054" ]
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008368.seq
d234331df96da49d2b9ab92cf42b63ed
A008369
Number of orbits on points that are at n steps from 0 in D_4 lattice.
[ "1", "1", "4", "6", "11", "16", "25", "33", "47", "60", "79", "98", "124" ]
[ "nonn" ]
15
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008369.seq
90478d7e0bf56d2cb6f3b06dbabf7bb4
A008370
Number of orbits on points that are at n steps from 0 in D_5 lattice.
[ "1", "1", "4", "7", "14", "22", "37", "53", "80", "109", "153", "200", "267" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008370.seq
d55a4712eb57e0cfe498af80db2b3ecf
A008371
Number of orbits on points that are at n steps from 0 in D_6 lattice.
[ "1", "1", "4", "8", "16", "27", "47", "72", "112", "163", "235", "325", "448" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008371.seq
6eb77556c4bc02d0b365db41d70ac3a9
A008372
Number of orbits on points that are at n steps from 0 in D_7 lattice.
[ "1", "1", "4", "8", "17", "30", "54", "86", "139", "209", "313", "448", "638" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008372.seq
ffa3bcec2e99e419cf5d507cf7ac08ae
A008373
Number of orbits on points that are at n steps from 0 in D_8 lattice.
[ "1", "1", "4", "8", "18", "32", "59", "97", "160", "248", "380", "560", "816" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008373.seq
3f2c324c28ea75a02f759d1cb0ba6fa9
A008374
Number of orbits on points that are at n steps from 0 in D_9 lattice.
[ "1", "1", "4", "8", "18", "33", "62", "104", "175", "277", "433", "651", "969" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008374.seq
ea604f87e000255148deef3aec6668b3
A008375
Number of orbits on points that are at n steps from 0 in D_10 lattice.
[ "1", "1", "4", "8", "18", "34", "64", "109", "186", "299", "474", "725", "1094" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane and J. H. Conway
2016-10-09T09:34:16
oeisdata/seq/A008/A008375.seq
86bd543d22a80a78e98e8ba11564f1d1
A008376
Coordination sequence for D_9 lattice.
[ "1", "144", "4194", "50832", "361602", "1801872", "6976866", "22413456", "62407170", "155242640", "352624482", "743284368", "1471858818", "2764261008", "4960898658", "8559218832", "14267189250", "23069454480", "36308034146", "55779559056", "83851169922", "123597332112", "178959948642", "254934282384", "357783327234" ]
[ "nonn", "easy" ]
27
0
2
[ "A008376", "A103903" ]
null
N. J. A. Sloane and J. H. Conway
2023-09-06T01:42:26
oeisdata/seq/A008/A008376.seq
dc7439103f6c21433f66918fec07dee8
A008377
Crystal ball sequence for D_9 lattice.
[ "1", "145", "4339", "55171", "416773", "2218645", "9195511", "31608967", "94016137", "249258777", "601883259", "1345167627", "2817026445", "5581287453", "10542186111", "19101404943", "33368594193", "56438048673", "92746082819", "148525641875", "232376811797", "355974143909", "534934092551", "789868374935" ]
[ "nonn", "easy" ]
32
0
2
null
null
N. J. A. Sloane and J. H. Conway
2024-05-11T05:15:17
oeisdata/seq/A008/A008377.seq
9757decd922c259284ba4ca1b244475a
A008378
Coordination sequence for D_10 lattice.
[ "1", "180", "6440", "94620", "802640", "4687108", "20924280", "76392940", "238753440", "659632980", "1649142216", "3796582460", "8156356080", "16522765220", "31822575640", "58659933324", "104054451520", "178420035060", "296839277160", "480696051420", "759737228432", "1174643272260", "1780196817080" ]
[ "nonn", "easy" ]
31
0
2
[ "A008378", "A008379", "A103903" ]
null
N. J. A. Sloane and J. H. Conway
2024-02-07T09:36:10
oeisdata/seq/A008/A008378.seq
cdd5aec1bb1d4cccb5cdec24b142ca44
A008379
Crystal ball sequence for D_10 lattice.
[ "1", "181", "6621", "101241", "903881", "5590989", "26515269", "102908209", "341661649", "1001294629", "2650436845", "6447019305", "14603375385", "31126140605", "62948716245", "121608649569", "225663101089", "404083136149", "700922413309", "1181618464729", "1941355693161", "3115998965421", "4896195782501" ]
[ "nonn", "easy" ]
29
0
2
null
null
N. J. A. Sloane and J. H. Conway
2024-02-07T09:36:06
oeisdata/seq/A008/A008379.seq
03c68bb09c72ad0667833608553962a0
A008380
4*(2n-1)!*H(2n), where H(n) = Sum 1/i are harmonic numbers.
[ "6", "50", "1176", "54792", "4251456", "495480960", "80990184960", "17683570598400", "4972664013004800", "1750589607352320000", "754268505333719040000", "390464536066453094400000", "239146855253471119933440000" ]
[ "nonn" ]
6
1
1
null
null
N. J. A. Sloane.
2012-03-30T16:45:19
oeisdata/seq/A008/A008380.seq
883ea104de5bc915e49761564d9e345e
A008381
floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5).
[ "0", "0", "0", "0", "0", "1", "1", "2", "4", "8", "16", "16", "24", "36", "54", "81", "81", "108", "144", "192", "256", "256", "320", "400", "500", "625", "625", "750", "900", "1080", "1296", "1296", "1512", "1764", "2058", "2401", "2401", "2744", "3136", "3584", "4096", "4096", "4608", "5184", "5832" ]
[ "nonn" ]
5
0
8
null
null
N. J. A. Sloane.
2012-03-30T17:38:27
oeisdata/seq/A008/A008381.seq
83fe699d2718ca0460fb75c8b4dbee9a
A008382
a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5)*floor((n+4)/5).
[ "0", "0", "0", "0", "0", "1", "2", "4", "8", "16", "32", "48", "72", "108", "162", "243", "324", "432", "576", "768", "1024", "1280", "1600", "2000", "2500", "3125", "3750", "4500", "5400", "6480", "7776", "9072", "10584", "12348", "14406", "16807", "19208", "21952", "25088", "28672", "32768", "36864", "41472", "46656", "52488", "59049", "65610", "72900", "81000" ]
[ "nonn" ]
43
0
7
[ "A000584", "A002620", "A006501", "A008233", "A008382", "A008881", "A009641", "A009694", "A009714", "A013663", "A354600" ]
null
N. J. A. Sloane
2023-01-10T07:59:38
oeisdata/seq/A008/A008382.seq
66733ac77731105f448f9fa82bb7be0b
A008383
Coordination sequence for A_4 lattice.
[ "1", "20", "110", "340", "780", "1500", "2570", "4060", "6040", "8580", "11750", "15620", "20260", "25740", "32130", "39500", "47920", "57460", "68190", "80180", "93500", "108220", "124410", "142140", "161480", "182500", "205270", "229860", "256340", "284780", "315250", "347820", "382560", "419540", "458830", "500500", "544620" ]
[ "nonn", "easy" ]
43
0
2
[ "A005901", "A008383", "A008384", "A008385" ]
null
N. J. A. Sloane and J. H. Conway
2023-12-10T16:05:19
oeisdata/seq/A008/A008383.seq
857f0ef16d20e3e1bb1890b37ef42c55
A008384
Crystal ball sequence for A_4 lattice.
[ "1", "21", "131", "471", "1251", "2751", "5321", "9381", "15421", "24001", "35751", "51371", "71631", "97371", "129501", "169001", "216921", "274381", "342571", "422751", "516251", "624471", "748881", "891021", "1052501", "1235001", "1440271" ]
[ "nonn", "nice", "easy" ]
37
0
2
[ "A008383", "A008384" ]
null
N. J. A. Sloane and J. H. Conway
2024-08-06T04:37:58
oeisdata/seq/A008/A008384.seq
00f43c7a8edb77fc94eae1ebdea558b5
A008385
Coordination sequence for A_5 lattice.
[ "1", "30", "240", "1010", "2970", "7002", "14240", "26070", "44130", "70310", "106752", "155850", "220250", "302850", "406800", "535502", "692610", "882030", "1107920", "1374690", "1687002", "2049770", "2468160", "2947590", "3493730", "4112502", "4810080", "5592890", "6467610", "7441170", "8520752" ]
[ "nonn", "easy" ]
37
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-12-13T10:53:10
oeisdata/seq/A008/A008385.seq
79a234c031922febaec28df760434b3d
A008386
Crystal ball sequence for A_5 lattice.
[ "1", "31", "271", "1281", "4251", "11253", "25493", "51563", "95693", "166003", "272755", "428605", "648855", "951705", "1358505", "1894007", "2586617", "3468647", "4576567", "5951257", "7638259", "9688029", "12156189", "15103779", "18597509" ]
[ "nonn", "easy" ]
26
0
2
null
null
N. J. A. Sloane and J. H. Conway
2018-04-08T16:20:33
oeisdata/seq/A008/A008386.seq
bec9644f71baca8f4030e1c26c58466b
A008387
Coordination sequence for A_6 lattice.
[ "1", "42", "462", "2562", "9492", "27174", "65226", "137886", "264936", "472626", "794598", "1272810", "1958460", "2912910", "4208610", "5930022", "8174544", "11053434", "14692734", "19234194", "24836196", "31674678", "39944058", "49858158", "61651128", "75578370", "91917462", "110969082" ]
[ "nonn", "easy" ]
40
0
2
[ "A008387", "A103881" ]
null
N. J. A. Sloane and J. H. Conway
2023-12-13T10:54:40
oeisdata/seq/A008/A008387.seq
c69ca5cbb3b5b05e97407620af9fffa4
A008388
Crystal ball sequence for A_6 lattice.
[ "1", "43", "505", "3067", "12559", "39733", "104959", "242845", "507781", "980407", "1775005", "3047815", "5006275", "7919185", "12127795", "18057817", "26232361", "37285795", "51978529", "71212723", "96048919", "127723597", "167667655" ]
[ "nonn", "easy" ]
30
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-05-28T10:27:10
oeisdata/seq/A008/A008388.seq
2022c6159659ab5736f39cbb418cf93b
A008389
Coordination sequence for A_7 lattice.
[ "1", "56", "812", "5768", "26474", "91112", "256508", "623576", "1356194", "2703512", "5025692", "8823080", "14768810", "23744840", "36881420", "55599992", "81659522", "117206264", "164826956", "227605448", "309182762", "413820584", "546468188", "712832792", "919453346" ]
[ "nonn", "easy" ]
39
0
2
[ "A008389", "A103881" ]
null
N. J. A. Sloane and J. H. Conway
2024-08-11T23:24:08
oeisdata/seq/A008/A008389.seq
20e572b3df5cfc8796a0034b5d5ad72f
A008390
Crystal ball sequence for A_7 lattice.
[ "1", "57", "869", "6637", "33111", "124223", "380731", "1004307", "2360501", "5064013", "10089705", "18912785", "33681595", "57426435", "94307855", "149907847", "231567369", "348773633", "513600589", "741206037", "1050388799", "1464209383" ]
[ "nonn" ]
22
0
2
null
null
N. J. A. Sloane and J. H. Conway
2017-12-16T15:15:56
oeisdata/seq/A008/A008390.seq
e0de7d3e197779766518821e851837c6
A008391
Coordination sequence for A_8 lattice.
[ "1", "72", "1332", "11832", "66222", "271224", "889716", "2476296", "6077196", "13507416", "27717948", "53265960", "96900810", "168278760", "280819260", "452715672", "708113304", "1078467624", "1604095524", "2335932504", "3337508646", "4687156248", "6480461988", "8832976488", "11883194148", "15795816120" ]
[ "nonn", "easy" ]
46
0
2
[ "A008391", "A103881" ]
null
N. J. A. Sloane and J. H. Conway
2023-05-27T03:15:32
oeisdata/seq/A008/A008391.seq
7ede363cb54a6194c61beaf23cb93274
A008392
Crystal ball sequence for A_8 lattice.
[ "1", "73", "1405", "13237", "79459", "350683", "1240399", "3716695", "9793891", "23301307", "51019255", "104285215", "201186025", "369464785", "650284045", "1102999717", "1811113021", "2889580645", "4493676169", "6829608673", "10167117319", "14854273567", "21334735555", "30167712043", "42050906191", "57846722311" ]
[ "nonn", "easy" ]
29
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-05-27T02:09:37
oeisdata/seq/A008/A008392.seq
d75551d90798d0a27e825b8e5cc58de2
A008393
Coordination sequence for A_9 lattice.
[ "1", "90", "2070", "22530", "151560", "731502", "2777370", "8809110", "24314490", "60110030", "135916002", "285510150", "563873400", "1056789450", "1893408750", "3262336002", "5431848930", "8774904690", "13799638910", "21186110970", "31830097752", "46894786710" ]
[ "nonn", "easy" ]
29
0
2
[ "A008393", "A103881" ]
null
N. J. A. Sloane and J. H. Conway
2023-05-30T14:11:30
oeisdata/seq/A008/A008393.seq
212fa34e4ec2ef3e9b45ca7c531a6c85
A008394
Crystal ball sequence for A_9 lattice.
[ "1", "91", "2161", "24691", "176251", "907753", "3685123", "12494233", "36808723", "96918753", "232834755", "518344905", "1082218305", "2139007755", "4032416505", "7294752507", "12726601437", "21501506127", "35301145037", "56487256007" ]
[ "nonn" ]
40
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-05-28T02:00:19
oeisdata/seq/A008/A008394.seq
a7fff33f899f89fddc9dc9690319816f
A008395
Coordination sequence for A_10 lattice.
[ "1", "110", "3080", "40370", "322190", "1815506", "7925720", "28512110", "88206140", "241925530", "601585512", "1379301990", "2953859370", "5968878630", "11472968760", "21114177018", "37403270520", "64062783510", "106481351240", "172295622730", "272125000774", "420487598410" ]
[ "nonn", "easy" ]
40
0
2
[ "A008395", "A103881" ]
null
N. J. A. Sloane and J. H. Conway
2023-05-28T04:04:47
oeisdata/seq/A008/A008395.seq
ca9743677c8e1d9ed16a967dfb1d3f07
A008396
Crystal ball sequence for A_10 lattice.
[ "1", "111", "3191", "43561", "365751", "2181257", "10106977", "38619087", "126825227", "368750757", "970336269", "2349638259", "5303497629", "11272376259", "22745345019", "43859522037", "81262792557", "145325576067", "251806927307" ]
[ "nonn", "easy" ]
29
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-05-30T14:11:38
oeisdata/seq/A008/A008396.seq
d0a9dc96e8045ee512ad48da31584d57
A008397
Coordination sequence for E_7 lattice.
[ "1", "126", "2898", "25886", "133506", "490014", "1433810", "3573054", "7902594", "15942206", "29896146", "52834014", "88892930", "143501022", "223622226", "338022398", "497556738", "715478526", "1007769170", "1393489566" ]
[ "nonn", "easy" ]
38
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-05-30T14:11:26
oeisdata/seq/A008/A008397.seq
8c2c967a190223c6d8984d836a797ee7
A008398
Crystal ball sequence for E_7 lattice.
[ "1", "127", "3025", "28911", "162417", "652431", "2086241", "5659295", "13561889", "29504095", "59400241", "112234255", "201127185", "344628207", "568250433", "906272831", "1403829569", "2119308095", "3127077265", "4520566831", "6415719601", "8954837583", "12310843425", "16691978463", "22346958689", "29570609951" ]
[ "nonn", "easy", "nice" ]
39
0
2
null
null
N. J. A. Sloane and J. H. Conway
2024-05-28T12:35:51
oeisdata/seq/A008/A008398.seq
fedfa1f15a8653b4280beb8afd69d3c8
A008399
Coordination sequence for E_6 lattice.
[ "1", "72", "1062", "6696", "26316", "77688", "189810", "405720", "785304", "1408104", "2376126", "3816648", "5885028", "8767512", "12684042", "17891064", "24684336", "33401736", "44426070", "58187880", "75168252", "95901624", "120978594", "151048728", "186823368", "229078440", "278657262", "336473352", "403513236" ]
[ "nonn", "easy" ]
43
0
2
[ "A008340", "A008397", "A008399", "A019557", "A019558" ]
null
N. J. A. Sloane and J. H. Conway
2023-12-10T16:06:07
oeisdata/seq/A008/A008399.seq
4d19e486478fd6fa773f6c4e360acb6b
A008400
Crystal ball sequence for E_6 lattice.
[ "1", "73", "1135", "7831", "34147", "111835", "301645", "707365", "1492669", "2900773", "5276899", "9093547", "14978575", "23746087", "36430129", "54321193", "79005529", "112407265", "156833335", "215021215", "290189467", "386091091" ]
[ "nonn", "easy", "nice" ]
35
0
2
null
null
N. J. A. Sloane and J. H. Conway
2023-12-10T16:07:42
oeisdata/seq/A008/A008400.seq
853b0cb63bf6daf7746c79c4f38a1769