A016256 Expansion of 1/((1-x)*(1-8*x)*(1-9*x)).

1, 18, 235, 2700, 28981, 298278, 2984095, 29253600, 282456361, 2695498938, 25486623955, 239196683700, 2231306698141, 20710052641998, 191416812647815, 1762962024789000, 16188343910770321, 148268580698287458, 1355005110295423675, 12359749064745505500

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (18,-89,72)

Formula

G.f.: 1/((1-x)*(1-8*x)*(1-9*x)).

a(n) = 17*a(n-1) - 72*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011

a(n) = 9^(n+2)/8 - 8^(n+2)/7 + 1/56. - R. J. Mathar, Mar 14 2011

a(n) = 18*a(n-1) - 89*a(n-2) + 72*a(n-3). - Wesley Ivan Hurt, Apr 20 2023

Maple

a:=n->sum(9^(n-j)-8^(n-j), j=0..n): seq(a(n), n=1..19); # Zerinvary Lajos, Jan 04 2007

Mathematica

Table[(-8^(n + 2) + 7*9^(n + 1) + 1)/56, {n, 40}] (* and *) CoefficientList[Series[1/((1 - z) (1 - 8*z) (1 - 9*z)), {z, 0, 40}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)

Prog

(PARI) Vec(1/((1-x)*(1-8*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

Crossrefs

Cf. A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125.

Sequence in context: A021094 A275963 A125453 * A017065 A016252 A016301

Adjacent sequences: A016253 A016254 A016255 * A016257 A016258 A016259

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved