A021674 Expansion of 1/((1-x)(1-3x)(1-8x)(1-12x)).

1, 24, 397, 5676, 75529, 966048, 12071269, 148688052, 1814929057, 22024557672, 266258052541, 3210803780028, 38655303353785, 464868906584496, 5586469016901013, 67101965327432004, 805738280990712913

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (24,-179,444,-288).

Formula

G.f.: 1/((1-x)*(1-3*x)*(1-8*x)*(1-12*x)).

a(n) = -1/154 +3^(n+1)/10 -2^(3n+7)/35 +2^(2n+4)*3^(n+1)/11. [Bruno Berselli, May 07 2013]

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 3 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* Bruno Berselli, May 07 2013 *)
LinearRecurrence[{24, -179, 444, -288}, {1, 24, 397, 5676}, 20] (* Harvey P. Dale, Oct 16 2020 *)

Prog

(PARI) Vec(1/((1-x)*(1-3*x)*(1-8*x)*(1-12*x))+O(x^20)) \\ Bruno Berselli, May 07 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-8*x)*(1-12*x)))); // Bruno Berselli, May 07 2013

Crossrefs

Cf. A018071 (first differences).

Sequence in context: A021694 A019687 A020341 * A019677 A021314 A018206

Adjacent sequences: A021671 A021672 A021673 * A021675 A021676 A021677

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved