A018071 Expansion of 1/((1-3x)(1-8x)(1-12x)).

1, 23, 373, 5279, 69853, 890519, 11105221, 136616783, 1666241005, 20209628615, 244233494869, 2944545727487, 35444499573757, 426213603230711, 5121600110316517, 61515496310530991, 738636315663280909

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-156,288).

Formula

a(0)=1, a(1)=23, a(2)=373; for n>2, a(n) = 23*a(n-1) -156*a(n-2) +288*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 20*a(n-1) -96*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (5*12^(n+2) - 9*8^(n+2) + 4*3^(n+2))/180. [Yahia Kahloune, Jul 06 2013]

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 8 x) (1 - 12 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{23, -156, 288}, {1, 23, 373}, 30] (* Harvey P. Dale, Aug 27 2014 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-8*x)*(1-12*x)))); * or */ I:=[1, 23, 373]; [n le 3 select I[n] else 23*Self(n-1)-156*Self(n-2)+288*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A019628 A018091 A021279 * A016325 A016324 A264321

Adjacent sequences: A018068 A018069 A018070 * A018072 A018073 A018074

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved