A099110 Expansion of 1 / ((1+x)*(1-2x)*(1-3x)*(1-4x)).

1, 8, 47, 238, 1113, 4956, 21379, 90266, 375485, 1545544, 6313671, 25650534, 103792417, 418745972, 1685723723, 6775136242, 27197312709, 109079641440, 437189912335, 1751374038590, 7013340021161, 28076893083148

Offset: 0

Author

Ralf Stephan, Sep 28 2004

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-17,-2,24).

Crossrefs

First differences are in A004057. Pairwise sums are in A016269.

Programs

Mathematica

CoefficientList[Series[1/((1+x)(1-2x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{8,-17,-2,24},{1,8,47,238},30] (* Harvey P. Dale, Oct 03 2016 *)

PARI

Vec(1/((1+x)*(1-2*x)*(1-3*x)*(1-4*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = (1/60) (80*2^n - 405*3^n + 384*4^n + (-1)^n).

a(n) = 8*a(n-1) - 17*a(n-2) - 2*a(n-3) + 24*a(n-4), n >= 4. - Vincenzo Librandi, Mar 22 2011