A018092 Expansion of 1/((1-3*x)*(1-9*x)*(1-12*x)).

1, 24, 405, 5940, 81081, 1061424, 13533885, 169579980, 2099526561, 25775439624, 314535422565, 3821496571620, 46281602898441, 559192032726624, 6744619579010445, 81244271639092860, 977710789930868721

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24, -171, 324).

Formula

a(n) = 24*a(n-1) - 171*a(n-2) + 324*a(n-3); a(1)=1, a(2)=24, a(3)=405. - Harvey P. Dale, Apr 26 2011

a(n) = (32*4^n - 27*3^n + 1)*3^(n-1)/2. - Bruno Berselli, May 16 2011

Mathematica

LinearRecurrence[{24, -171, 324}, {1, 24, 405}, 30] (* or *)
CoefficientList[Series[1/((1-3x)(1-9x)(1-12x)), {x, 0, 30}], x]  (* Harvey P. Dale, Apr 26 2011 *)

Prog

(Magma) [(32*4^n-27*3^n+1)*3^(n-1)/2 : n in [0..20]]; // Vincenzo Librandi, May 17 2011
(PARI) Vec(1/((1-3*x)*(1-9*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A021314 A018206 A021304 * A331931 A227750 A221619

Adjacent sequences: A018089 A018090 A018091 * A018093 A018094 A018095

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved