A020983 Expansion of 1/((1-9*x)*(1-10*x)*(1-12*x)).

1, 31, 643, 11155, 174811, 2566291, 36012523, 489103555, 6481822171, 84295081651, 1080159920203, 13679489505955, 171612008243131, 2136467306462611, 26431716545456683, 325327578356628355, 3987253758579873691, 48696950467661485171, 593012553894264829963

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..920

Index entries for linear recurrences with constant coefficients, signature (31,-318,1080)

Formula

a(n) = 31*a(n-1) - 318*a(n-2) + 1080*a(n-3), n >= 3. - Vincenzo Librandi, Mar 18 2011

a(n) = 22*a(n-1) - 120*a(n-2) + 9^n, n >= 2. - Vincenzo Librandi, Mar 18 2011

a(n) = -5*10^(n+1) + 3*9^(n+1) + 2*12^(n+1). - R. J. Mathar, Mar 20 2011

Mathematica

CoefficientList[Series[1/((1-9*x)*(1-10*x)*(1-12*x)), {x, 0, 50}], x] (* G. C. Greubel, Feb 09 2018 *)
LinearRecurrence[{31, -318, 1080}, {1, 31, 643}, 20] (* Robert G. Wilson v, Feb 11 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(1/((1-9*x)*(1-10*x)*(1-12*x))) \\ G. C. Greubel, Feb 09 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!(1/((1-9*x)*(1-10*x)*(1-12*x)))); // G. C. Greubel, Feb 09 2018

Crossrefs

Sequence in context: A028004 A025007 A024446 * A020981 A362512 A006097

Adjacent sequences: A020980 A020981 A020982 * A020984 A020985 A020986

Keyword

nonn

Author

N. J. A. Sloane

Status

approved