A022291 Expansion of 1/((1-x)(1-5x)(1-6x)(1-9x)).

1, 21, 292, 3402, 36043, 360843, 3485854, 32899944, 305751325, 2812114305, 25683350056, 233457113526, 2115260975647, 19123756383207, 172639882457698, 1556953539144948, 14031940169321809, 126404565100316349

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-149,399,-270).

Formula

a(0)=1, a(1)=21, a(2)=292, a(3)=3402; for n>3, a(n) = 21*a(n-1) -149*a(n-2) +399*a(n-3) -270*a(n-4). - Vincenzo Librandi, Jul 12 2013

a(n) = (5*9^(n+3) - 32*6^(n+3) + 30*5^(n+3) - 3)/480. [Yahia Kahloune, Aug 13 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 6 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)

Prog

(Magma) I:=[1, 21, 292, 3402]; [n le 4 select I[n] else 21*Self(n-1)-149*Self(n-2)+399*Self(n-3)-270*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-6*x)*(1-9*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) a(n) = (5*9^(n+3) - 32*6^(n+3) + 30*5^(n+3) - 3)/480; \\ Joerg Arndt, Aug 13 2013

Crossrefs

Sequence in context: A230021 A101700 A275359 * A025944 A025962 A181381

Adjacent sequences: A022288 A022289 A022290 * A022292 A022293 A022294

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved