A016217 Expansion of 1 / ((1-x) * (1-3*x) * (1-12*x)).

1, 16, 205, 2500, 30121, 361816, 4342885, 52117900, 625424641, 7505125216, 90061591165, 1080739359700, 12968873113561, 155626479754216, 1867517764225045, 22410213192223900, 268922558371256881, 3227070700648792816, 38724848408366644525, 464698180902143126500

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (16, -51, 36).

Programs

Maple

a:= n-> add((12^(n+1-j)-3^(n+1-j))/9, j=0..n): seq(a(n), n=0..20); # Zerinvary Lajos, Jan 12 2007

Mathematica

CoefficientList[Series[1/((1-x)(1-3x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{16,-51,36},{1,16,205},30] (* Harvey P. Dale, May 06 2012 *)

Formula

a(0)=1, a(1)=16, a(n)=15*a(n-1)-36*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(0)=1, a(1)=16, a(2)=205, a(n)=16*a(n-1)-51*a(n-2)+36*a(n-3). - Harvey P. Dale, May 06 2012

a(n) = 1/22-(1/2)*3^n+(16/11)*12^n. - Antonio Alberto Olivares, May 12 2012