A016312 Expansion of 1/((1-2x)*(1-7x)*(1-9x)).

1, 18, 229, 2538, 26197, 259290, 2498293, 23637546, 220808533, 2043771642, 18789409717, 171872944074, 1566234297109, 14231753285274, 129035291862901, 1167964212866922, 10558204018573525, 95349518886691386

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-95,126).

Formula

a(n) = ((9^n - 2^n)/7 - (7^n - 2^n)/5)/2, n >= 2. - Zerinvary Lajos, Jun 05 2009

a(n) = 18*a(n-1) - 95*a(n-2) + 126*a(n-3). - Vincenzo Librandi, Jun 26 2013

Mathematica

CoefficientList[Series[1 / ((1 - 2 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 26 2013 *)

Prog

(Sage) [((9^n - 2^n)/7-(7^n - 2^n)/5)/2 for n in range(2, 20)] # Zerinvary Lajos, Jun 05 2009
(Magma) I:=[1, 18, 229]; [n le 3 select I[n] else 18*Self(n-1)-95*Self(n-2)+126*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-7*x)*(1-9*x)))); // Vincenzo Librandi, Jun 26 2013
(PARI) x='x+O('x^99); Vec(1/((1-2*x)*(1-7*x)*(1-9*x))) \\ Altug Alkan, Sep 21 2018

Crossrefs

Sequence in context: A021144 A296854 A296941 * A017916 A016307 A193982

Adjacent sequences: A016309 A016310 A016311 * A016313 A016314 A016315

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved