A016278 Expansion of 1/((1-2x)(1-3x)(1-9x)).

1, 14, 145, 1370, 12541, 113534, 1023865, 9221090, 83008981, 747138854, 6724424785, 60520350410, 544684739821, 4902167424974, 44119521140905, 397075733249330, 3573681728253061, 32163135941435894, 289468224634660225

Offset

0,2

Links

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

Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Counting families of generalized balancing numbers, The Australasian Journal of Combinatorics (2020) Vol. 77, Part 3, 318-325.

Index entries for linear recurrences with constant coefficients, signature (14,-51,54).

Formula

a(n) = 14*a(n-1) - 51*a(n-2) + 54*a(n-3); a(n) = (4/7)*2^(n-1) + (-3/2)*3^(n-1) + (27/14)*9^(n-1). - Antonio Alberto Olivares, Apr 21 2008, Apr 22 2008

Mathematica

CoefficientList[Series[1 / ((1 - 2 x) (1 - 3 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 24 2013 *)

Prog

(PARI) Vec(1/((1-2*x)*(1-3*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-3*x)*(1-9*x)))); // Vincenzo Librandi, Jun 24 2013

Crossrefs

Cf. A053141, A053142.

Sequence in context: A016233 A276250 A099914 * A241169 A209347 A132934

Adjacent sequences: A016275 A016276 A016277 * A016279 A016280 A016281

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved