A020981 Expansion of 1/((1-8*x)*(1-11*x)*(1-12*x)).

1, 31, 645, 11255, 177821, 2636991, 37440565, 515147335, 6923011341, 91364030351, 1188608942885, 15286543614615, 194762842152061, 2462271368182111, 30927944350627605, 386358083836485095

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (31,-316,1056).

Formula

a(n) = 16*8^n/3 -121*11^n/3 +36*12^n. - R. J. Mathar, Jul 01 2013

a(0)=1, a(1)=31, a(2)=645; for n>2, a(n) = 31*a(n-1) -316*a(n-2) +1056*a(n-3). - Vincenzo Librandi, Jul 05 2013

a(n) = 23*a(n-1) -132*a(n-2) +8^n. - Vincenzo Librandi, Jul 05 2013

Mathematica

CoefficientList[Series[1 / ((1 - 8 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)
LinearRecurrence[{31, -316, 1056}, {1, 31, 645}, 20] (* Harvey P. Dale, Apr 06 2023 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 31, 645]; [n le 3 select I[n] else 31*Self(n-1)-316*Self(n-2)+1056*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 05 2013
(PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-11*x)*(1-12*x))) \\ G. C. Greubel, Feb 09 2018

Crossrefs

Sequence in context: A025007 A024446 A020983 * A362512 A006097 A000565

Adjacent sequences: A020978 A020979 A020980 * A020982 A020983 A020984

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved