A016228 Expansion of 1/((1-x)*(1-5*x)(1-6*x)).

1, 12, 103, 774, 5425, 36456, 238267, 1527258, 9651829, 60352380, 374321311, 2306963022, 14146953913, 86407602384, 526075008835, 3194597025666, 19358317017277, 117103576420068, 707389830102439, 4268180838524790, 25728294320699521, 154965812371951032

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-41,30).

Crossrefs

Cf. A016218.

Programs

Maple

a:=n->sum(6^(n-j)-5^(n-j),j=0..n): seq(a(n), n=1..19); # Zerinvary Lajos, Jan 15 2007

Mathematica

Table[(2^(n + 3)*3^(n + 1) - 5^(n + 2) + 1)/20, {n, 40}] (* and *) CoefficientList[Series[1/((1 - z) (1 - 5*z) (1 - 6*z)), {z, 0, 40}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)
LinearRecurrence[{12,-41,30},{1,12,103},30] (* Harvey P. Dale, Aug 24 2017 *)

PARI

Vec(1/((1-x)*(1-5*x)(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = (1/20)-(25/4)*5^n+(36/5)*6^n. [Antonio Alberto Olivares, Feb 06 2010]

a(0)=1, a(1)=12, a(n)=11*a(n-1)-30*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011