A145133 Expansion of x/((1 - x - x^4)*(1 - x)^4).

0, 1, 5, 15, 35, 71, 132, 231, 386, 622, 974, 1491, 2241, 3318, 4852, 7023, 10080, 14367, 20359, 28712, 40332, 56470, 78853, 109865, 152797, 212192, 294321, 407840, 564697, 781384, 1080665, 1493961, 2064642, 2852571, 3940376, 5442107, 7515185

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 5th row of A145152.

Examples

			a(9) = 622 = 5*386 -10*231 +10*132 -4*71 -3*35 +6*15 -4*5 +1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -4, -3, 6, -4, 1).

Crossrefs

5th 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(5): seq (a(n), n=0..40);

Mathematica

CoefficientList[Series[x/((1-x-x^4)*(1-x)^4),{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,10,-4,-3,6,-4,1},{0,1,5,15,35,71,132,231},40] (* Harvey P. Dale, Oct 24 2011 *)

PARI

Vec(1/((1 - x - x^4)*(1 - x)^4)+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012

Formula

a(n) = 5a(n-1) -10a(n-2) +10a(n-3) -4a(n-4) -3a(n-5) +6a(n-6) -4a(n-7) +a(n-8).