A145135 Expansion of x/((1 - x - x^4)*(1 - x)^6).

0, 1, 7, 28, 84, 211, 470, 960, 1836, 3334, 5806, 9769, 15973, 25495, 39869, 61266, 92743, 138587, 204790, 299705, 434952, 626669, 897239, 1277674, 1810906, 2556330, 3596075, 5043660, 7055942, 9849608, 13723939, 19092231, 26525165

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 7th row of A145152.

Links

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

Crossrefs

7th 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(7): seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x / ((1 - x - x^4) (1 - x)^6), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 06 2013 *)

PARI

concat(0,Vec(1/(1-x-x^4)/(1-x)^6+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(n) = 7a(n-1) -21a(n-2) +35a(n-3) -34a(n-4) +15a(n-5) +8a(n-6) -19a(n-7) +15a(n-8) -6a(n-9) +a(n-10).