A016234 Expansion of 1/((1-x)(1-5x)(1-9x)).

1, 15, 166, 1650, 15631, 144585, 1320796, 11984820, 108351661, 977606355, 8810664226, 79357013190, 714518294491, 6432190529325, 57897344158456, 521114244398760, 4690218934452121, 42212924084385495

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15, -59, 45).

Formula

a(0)=1, a(1)=15, a(n) = 14*a(n-1) - 45*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011

a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32. - Yahia Kahloune, Aug 13 2013

a(0)=1, a(1)=15, a(2)=166, a(n) = 15*a(n-1) - 59*a(n-2) + 45*a(n-3). - Harvey P. Dale, Oct 16 2014

O.g.f.: see the name.

E.g.f.: (d^2/dx^2) (exp(x)*((exp(4*x) - 1)^2)/(4^2*2!)) = exp(x)*(1 - 50*exp(4*x) + 81*exp(8*x))/32.

Mathematica

CoefficientList[Series[1/((1-x)(1-5x)(1-9x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -59, 45}, {1, 15, 166}, 30] (* Harvey P. Dale, Oct 16 2014 *)

Prog

(PARI) Vec(1/((1-x)*(1-5*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(PARI) a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32; \\ Joerg Arndt, Aug 13 2013

Crossrefs

Cf. A000012, A003463.

Sequence in context: A118093 A167615 A210326 * A160197 A055660 A121114

Adjacent sequences: A016231 A016232 A016233 * A016235 A016236 A016237

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved