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

%I #11 May 09 2023 12:06:20

%S 1,3,10,22,49,91,168,280,462,714,1092,1596,2310,3234,4488,6072,8151,

%T 10725,14014,18018,23023,29029,36400,45136,55692,68068,82824,99960,

%U 120156,143412,170544,201552,237405,278103,324786,377454,437437,504735,580888,665896

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

%H Colin Barker, <a href="/A299336/b299336.txt">Table of n, a(n) for n = 0..1000</a>

%H Jia Huang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Huang/huang8.html">Partially Palindromic Compositions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See p. 4.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).

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

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

%F 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.

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

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

%K nonn,easy

%O 0,2

%A _Colin Barker_, Feb 07 2018

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Last modified June 15 10:19 EDT 2024. Contains 373407 sequences. (Running on oeis4.)