A145137 Expansion of x/((1 - x - x^4)*(1 - x)^8).

0, 1, 9, 45, 165, 496, 1297, 3058, 6655, 13586, 26323, 48829, 87308, 151282, 255125, 420234, 678086, 1074525, 1675754, 2576688, 3912574, 5875129, 8734923, 12872391, 18820765, 27325469, 39426248, 56570687, 80771068, 114821057, 162594985

Offset

0,3

Comments

The coefficients of the recursion for a(n) are given by the 9th row of A145152.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -125, 118, -56, -20, 61, -55, 28, -8, 1).

Formula

a(n) = [9, -36, 84, -125, 118, -56, -20, 61, -55, 28, -8, 1] * [a(n-1), ..., a(n-12)].

Maple

col:= proc(k) local l, j, M, n; l:= `if`(k=0, [1, 0, 0, 1], [seq(coeff( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix(nops(l), (i, j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if`(k=0, n->(M^n)[2, 3], n->(M^n)[1, 2]) end: a:= col(9): seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x/((1-x-x^4)(1-x)^8), {x, 0, 40}], x] (* or *) LinearRecurrence[{9, -36, 84, -125, 118, -56, -20, 61, -55, 28, -8, 1}, {0, 1, 9, 45, 165, 496, 1297, 3058, 6655, 13586, 26323, 48829}, 40] (* Harvey P. Dale, Feb 22 2012 *)

Prog

(PARI) concat(0, Vec(1/((1-x-x^4)*(1-x)^8)+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012

Crossrefs

9th column of A145153. Cf. A145152.

Sequence in context: A229889 A243743 A145458 * A221142 A144902 A128643

Adjacent sequences: A145134 A145135 A145136 * A145138 A145139 A145140

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 03 2008

Status

approved