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