A214269 -id:A214269 - cp's OEIS frontend

A214273 Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal.

0, 2, 1, 8, 12, 23, 51, 90, 165, 295, 550, 952, 1682, 2974, 5151, 9007, 15530, 26848, 46194, 79404, 136092, 232622, 397633, 677892, 1154741, 1964078, 3337218, 5664428, 9605090, 16274305, 27548925, 46602325, 78775262, 133073729, 224662007, 379067097, 639250682

Offset: 5

Alois P. Heinz, Jul 09 2012

nonn

			a(6) = 2: [5,1]. [1,5].
a(7) = 1: [1,5,1].
a(8) = 8: [6,2], [5,2,1], [5,1,2], [2,6], [2,5,1], [2,1,5], [1,5,2], [1,2,5].
a(9) = 12: [5,3,1], [5,1,3], [5,1,2,1], [3,5,1], [3,1,5], [2,1,5,1], [1,5,3], [1,5,2,1], [1,5,1,2], [1,3,5], [1,2,5,1], [1,2,1,5].

Alois P. Heinz, Table of n, a(n) for n = 5..2000

Column k=4 of A214269.

a(n) ~ c * d^n, where d = 1.67058061397048614428193473494469299002584... is the root of the equation -4 + 5*d - 9*d^2 + 8*d^3 - 12*d^4 + 9*d^5 - 11*d^6 + 8*d^7 - 9*d^8 + 6*d^9 - 5*d^10 + 3*d^11 - 2*d^12 + d^13 = 0, c = 0.5575332183681935160094360162291847580554... . - Vaclav Kotesovec, Sep 01 2014

A214274 Number of compositions of n where the difference between largest and smallest parts equals 5 and adjacent parts are unequal.

Original entry on oeis.org

0, 2, 1, 8, 12, 23, 56, 95, 186, 349, 649, 1181, 2168, 3932, 7045, 12741, 22716, 40528, 72086, 127802, 226191, 399378, 704011, 1238513, 2176306, 3817950, 6689530, 11707266, 20465195, 35738757, 62350777, 108682236, 189279785, 329390352, 572788101, 995343179

Offset: 6

Alois P. Heinz, Jul 09 2012

nonn

			a(7) = 2: [6,1], [1,6].
a(8) = 1: [1,6,1].
a(9) = 8: [7,2], [6,2,1], [6,1,2], [2,7], [2,6,1], [2,1,6], [1,6,2], [1,2,6].
a(10) = 12: [6,3,1], [6,1,3], [6,1,2,1], [3,6,1], [3,1,6], [2,1,6,1], [1,6,3], [1,6,2,1], [1,6,1,2], [1,3,6], [1,2,6,1], [1,2,1,6].

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 6..2000 (first 250 terms from Alois P. Heinz)

Column k=5 of A214269.

a(n) ~ c * d^n, where d = 1.70794647064333012330..., c = 0.5176707727128993957... . - Vaclav Kotesovec, Sep 01 2014

A214275 Number of compositions of n where the difference between largest and smallest parts equals 6 and adjacent parts are unequal.

Original entry on oeis.org

0, 2, 1, 8, 12, 23, 56, 100, 191, 370, 703, 1280, 2409, 4437, 8076, 14821, 26895, 48760, 88102, 158831, 285490, 512395, 917768, 1640448, 2928758, 5220037, 9291968, 16519618, 29335963, 52038382, 92218708, 163272053, 288813272, 510469514, 901536574, 1591035005

Offset: 7

Alois P. Heinz, Jul 09 2012

nonn

			a(8) = 2: [7,1], [1,7].
a(9) = 1: [1,7,1].
a(10) = 8: [8,2], [7,2,1], [7,1,2], [2,8], [2,7,1], [2,1,7], [1,7,2], [1,2,7].
a(11) = 12: [7,3,1], [7,1,3], [7,1,2,1], [3,7,1], [3,1,7], [2,1,7,1], [1,7,3], [1,7,2,1], [1,7,1,2], [1,3,7], [1,2,7,1], [1,2,1,7].

Alois P. Heinz, Table of n, a(n) for n = 7..2000

Column k=6 of A214269.

A214276 Number of compositions of n where the difference between largest and smallest parts equals 7 and adjacent parts are unequal.

Original entry on oeis.org

0, 2, 1, 8, 12, 23, 56, 100, 196, 375, 724, 1334, 2508, 4678, 8593, 15871, 29048, 53125, 96779, 175921, 318915, 577064, 1042342, 1878814, 3382049, 6078454, 10910254, 19557912, 35020059, 62637612, 111921906, 199797264, 356348437, 635040273, 1130800760

Offset: 8

Alois P. Heinz, Jul 09 2012

nonn

			a(9) = 2: [8,1], [1,8].
a(10) = 1: [1,8,1].
a(11) = 8: [9,2], [8,2,1], [8,1,2], [2,9], [2,8,1], [2,1,8], [1,8,2], [1,2,8].
a(12) = 12: [8,3,1], [8,1,3], [8,1,2,1], [3,8,1], [3,1,8], [2,1,8,1], [1,8,3], [1,8,2,1], [1,8,1,2], [1,3,8], [1,2,8,1], [1,2,1,8].

Alois P. Heinz, Table of n, a(n) for n = 8..2000

Column k=7 of A214269.

A214277 Number of compositions of n where the difference between largest and smallest parts equals 8 and adjacent parts are unequal.

Original entry on oeis.org

0, 2, 1, 8, 12, 23, 56, 100, 196, 380, 729, 1355, 2562, 4777, 8834, 16388, 30110, 55297, 101217, 184784, 336450, 611563, 1109435, 2008818, 3632205, 6557010, 11821718, 21286582, 38285132, 68782625, 123450341, 221358100, 396561946, 709850307, 1269638737

Offset: 9

Alois P. Heinz, Jul 09 2012

nonn

			a(10) = 2: [9,1], [1,9].
a(11) = 1: [1,9,1].
a(12) = 8: [9,2,1], [9,1,2], [2,9,1], [2,10], [2,1,9], [10,2], [1,9,2], [1,2,9].
a(13) = 12: [9,3,1], [9,1,3], [9,1,2,1], [3,9,1], [3,1,9], [2,1,9,1], [1,9,3], [1,9,2,1], [1,9,1,2], [1,3,9], [1,2,9,1], [1,2,1,9].

Alois P. Heinz, Table of n, a(n) for n = 9..2000

Column k=8 of A214269.

A214278 Number of compositions of n where the difference between largest and smallest parts equals 9 and adjacent parts are unequal.

Original entry on oeis.org

0, 2, 1, 8, 12, 23, 56, 100, 196, 380, 734, 1360, 2583, 4831, 8933, 16629, 30627, 56359, 103401, 189241, 345386, 629284, 1144379, 2076985, 3764633, 6812624, 12312124, 22223544, 40067505, 72159773, 129826552, 233358096, 419077220, 751979608, 1348268372

Offset: 10

Alois P. Heinz, Jul 09 2012

nonn

			a(11) = 2: [10,1], [1,10].
a(12) = 1: [1,10,1].
a(13) = 8: [2,11], [2,10,1], [2,1,10], [11,2], [10,2,1], [10,1,2], [1,2,10], [1,10,2].
a(14) = 12: [3,10,1], [3,1,10], [2,1,10,1], [10,3,1], [10,1,3], [10,1,2,1], [1,3,10], [1,2,10,1], [1,2,1,10], [1,10,3], [1,10,2,1], [1,10,1,2].

Alois P. Heinz, Table of n, a(n) for n = 10..2000

Column k=9 of A214269.

A214279 Number of compositions of n where the difference between largest and smallest parts equals 10 and adjacent parts are unequal.

Original entry on oeis.org

0, 2, 1, 8, 12, 23, 56, 100, 196, 380, 734, 1365, 2588, 4852, 8987, 16728, 30868, 56876, 104463, 191425, 349855, 638239, 1162173, 2112115, 3833245, 6946126, 12570162, 22719408, 41016345, 73967704, 133257636, 239847038, 431310105, 774970862, 1391362755

Offset: 11

Alois P. Heinz, Jul 09 2012

nonn

			a(12) = 2: [11,1], [1,11].
a(13) = 1: [1,11,1].
a(14) = 8: [2,12], [2,11,1], [2,1,11], [12,2], [11,2,1], [11,1,2], [1,2,11], [1,11,2].
a(15) = 12: [3,11,1], [3,1,11], [2,1,11,1], [11,3,1], [11,1,3], [11,1,2,1], [1,3,11], [1,2,11,1], [1,2,1,11], [1,11,3], [1,11,2,1], [1,11,1,2].

Alois P. Heinz, Table of n, a(n) for n = 11..2000

Column k=10 of A214269.

cp's OEIS Frontend

A214273 Number of compositions of n where the difference between largest and smallest parts equals 4 and adjacent parts are unequal.

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A214274 Number of compositions of n where the difference between largest and smallest parts equals 5 and adjacent parts are unequal.

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A214275 Number of compositions of n where the difference between largest and smallest parts equals 6 and adjacent parts are unequal.

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A214276 Number of compositions of n where the difference between largest and smallest parts equals 7 and adjacent parts are unequal.

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A214277 Number of compositions of n where the difference between largest and smallest parts equals 8 and adjacent parts are unequal.

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A214278 Number of compositions of n where the difference between largest and smallest parts equals 9 and adjacent parts are unequal.

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A214279 Number of compositions of n where the difference between largest and smallest parts equals 10 and adjacent parts are unequal.

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