A019664 Expansion of 1/((1-4x)(1-8x)(1-9x)).

1, 21, 301, 3669, 40957, 433125, 4418317, 43942773, 428973853, 4128937989, 39306876973, 370937567637, 3475860284989, 32382187083813, 300235508341069, 2772487245505461, 25515330868003165, 234141560259529797

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,-140,288).

Formula

a(n) = 4^(n+1)/5+9^(n+2)/5-2*8^(n+1). - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=21, a(2)=301; for n>2, a(n) = 21*a(n-1) -140*a(n-2) +288*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 17*a(n-1) -72*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 8 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/((1-4*x)*(1-8*x)*(1-9*x)))); /* or */ I:=[1, 21, 301]; [n le 3 select I[n] else 21*Self(n-1)-140*Self(n-2)+288*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A025935 A077506 A007592 * A019839 A077513 A079517

Adjacent sequences: A019661 A019662 A019663 * A019665 A019666 A019667

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved