A020494 Expansion of 1/((1-5x)(1-9x)(1-10x)).

1, 24, 391, 5394, 67921, 808164, 9257851, 103242534, 1128792181, 12157176504, 129404822911, 1364594578074, 14281107062041, 148528742855244, 1536752582181571, 15830742722056014, 162476531910613501

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-185,450).

Formula

a(n) = 5*5^n/4 -81*9^n/4 +20*10^n. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=24, a(2)=391; for n>2, a(n) = 24*a(n-1) -185*a(n-2) +450*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 19*a(n-1) -90*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{24, -185, 450}, {1, 24, 391}, 20] (* Harvey P. Dale, Nov 27 2014 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-9*x)*(1-10*x)))); /* or */ I:=[1, 24, 391]; [n le 3 select I[n] else 24*Self(n-1)-185*Self(n-2)+450*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A020584 A025970 A021924 * A020573 A022448 A025947

Adjacent sequences: A020491 A020492 A020493 * A020495 A020496 A020497

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved