A299336 Expansion of 1 / ((1 - x)^7*(1 + x)^4).

1, 3, 10, 22, 49, 91, 168, 280, 462, 714, 1092, 1596, 2310, 3234, 4488, 6072, 8151, 10725, 14014, 18018, 23023, 29029, 36400, 45136, 55692, 68068, 82824, 99960, 120156, 143412, 170544, 201552, 237405, 278103, 324786, 377454, 437437, 504735, 580888, 665896

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See p. 4.

Index entries for linear recurrences with constant coefficients, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).

Formula

a(n) = (2*n^6 + 66*n^5 + 860*n^4 + 5640*n^3 + 19568*n^2 + 33984*n + 23040) / 23040 for n even.

a(n) = (2*n^6 + 66*n^5 + 860*n^4 + 5580*n^3 + 18578*n^2 + 28914*n + 15120) / 23040 for n odd.

a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11) for n>10.

Prog

(PARI) Vec(1 / ((1 - x)^7*(1 + x)^4) + O(x^40))

Crossrefs

Cf. A001769, A060099, A299335, A299337, A299338.

Sequence in context: A248851 A023554 A294414 * A222629 A070880 A321335

Adjacent sequences: A299333 A299334 A299335 * A299337 A299338 A299339

Keyword

nonn,easy

Author

Colin Barker, Feb 07 2018

Status

approved