A016204 Expansion of 1/((1-x)*(1-2*x)*(1-9*x)).

1, 12, 115, 1050, 9481, 85392, 768655, 6918150, 62263861, 560375772, 5043383995, 45390460050, 408514148641, 3676627354152, 33089646220135, 297806816046750, 2680261344551821, 24122352101228532, 217101168911581075

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-29,18).

Programs

Maple

A016204 := proc(n) (9^(n+2)-2^(n+5)+7)/56 ; end proc:
seq(A016204(n),n=0..20) ; # R. J. Mathar, Feb 09 2011

Mathematica

CoefficientList[Series[1/((1-x)(1-2x)(1-9x)),{x,0,40}],x] (* or *) LinearRecurrence[{12,-29,18},{1,12,115},40] (* Harvey P. Dale, Jun 05 2012 *)

PARI

Vec(1/((1-x)*(1-2*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = (81*9^n-32*2^n+7)/56. - Bruno Berselli, Feb 09 2011

a(n) = 9*a(n-1) + 2^(n+1) - 1. - Vincenzo Librandi, Feb 09 2011

a(0)=1, a(1)=12, a(2)=115, a(n) = 12*a(n-1) - 29*a(n-2) + 18*a(n-3). - Harvey P. Dale, Jun 05 2012