A019793 Expansion of 1/((1-5x)(1-6x)(1-9x)).

1, 20, 271, 3110, 32641, 324800, 3125011, 29414090, 272851381, 2506362980, 22871235751, 207773763470, 1881803862121, 17008495407560, 153516126074491, 1384313656687250, 12474986630176861, 112372624930994540

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-129,270).

Formula

a(n) = 25*5^n/4 -12*6^n +27*9^n/4. R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=20, a(2)=271; for n>2, a(n) = 20*a(n-1) -129*a(n-2) +270*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 15*a(n-1) -54*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 6 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-6*x)*(1-9*x)))); /* or */ I:=[1, 20, 271]; [n le 3 select I[n] else 20*Self(n-1)-129*Self(n-2)+270*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A180799 A021594 A224248 * A021774 A181384 A269009

Adjacent sequences: A019790 A019791 A019792 * A019794 A019795 A019796

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved