A145136 Expansion of x/((1 - x - x^4)*(1 - x)^7).

0, 1, 8, 36, 120, 331, 801, 1761, 3597, 6931, 12737, 22506, 38479, 63974, 103843, 165109, 257852, 396439, 601229, 900934, 1335886, 1962555, 2859794, 4137468, 5948374, 8504704, 12100779, 17144439, 24200381, 34049989, 47773928, 66866159, 93391324, 130201994

Offset: 0

Author

Alois P. Heinz, Oct 03 2008

Keywords

• nonn
• easy

Comments

The coefficients of the recursion for a(n) are given by the 8th row of A145152.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -69, 49, -7, -27, 34, -21, 7, -1).

Crossrefs

8th column of A145153. Cf. A145152.

Programs

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(8): seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x/((1-x-x^4)*(1-x)^7),{x,0,40}],x] (* or *) LinearRecurrence[{8,-28,56,-69,49,-7,-27,34,-21,7,-1},{0,1,8,36,120,331,801,1761,3597,6931,12737},40] (* Harvey P. Dale, Jan 03 2012 *)

PARI

concat(0,Vec(1/((1-x-x^4)*(1-x)^7)+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(n) = 8a(n-1) -28a(n-2) +56a(n-3) -69a(n-4) +49a(n-5) -7a(n-6) -27a(n-7) +34a(n-8) -21a(n-9) +7a(n-10) -a(n-11), with a(0)=0, a(1)=1, a(2)=8, a(3)=36, a(4)=120, a(5)=331, a(6)=801, a(7)=1761, a(8)=3597, a(9)=6931, a(10)=12737