A020595 Expansion of 1/((1-6x)(1-9x)(1-10x)).

1, 25, 421, 5965, 76741, 929005, 10791061, 121699645, 1342777381, 14569879885, 156038219701, 1653799781725, 17380932862021, 181408804717165, 1882561696208341, 19442349988398205, 199976918230722661

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-204,540).

Formula

a(0)=1, a(1)=25, a(2)=421; For n>2, a(n) = 25*a(n-1)-204*a(n-2)+540*a(n-3). - Harvey P. Dale, Oct 13 2012

a(n) = (3*10^(n+2) - 4*9^(n+2) + 6^(n+2))/12. [Yahia Kahloune, Jun 30 2013]

a(n) = 19*a(n-1) -90*a(n-2) +6^n. - Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1 / ((1 - 6 x) (1 - 9 x) (1 - 10 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{25, -204, 540}, {1, 25, 421}, 20] (* Harvey P. Dale, Oct 13 2012 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-9*x)*(1-10*x)))); /* or */ I:=[1, 25, 421]; [n le 3 select I[n] else 25*Self(n-1)-204*Self(n-2)+540*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Crossrefs

Sequence in context: A020838 A025975 A025953 * A001456 A021964 A022456

Adjacent sequences: A020592 A020593 A020594 * A020596 A020597 A020598

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved