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

1, 25, 421, 5965, 76741, 929005, 10791061, 121699645, 1342777381, 14569879885, 156038219701, 1653799781725, 17380932862021, 181408804717165, 1882561696208341, 19442349988398205, 199976918230722661, 2049766874087336845, 20947749526851028981, 213528831702049245085

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (25,-204,540).

Crossrefs

Cf. A016172, A016173.

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-9*x)*(1-10*x)))); // Vincenzo Librandi, Jul 04 2013

Magma

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

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 *)

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

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(6*x)*(300*exp(4*x) - 324*exp(3*x) + 36)/12.

a(n) = A016173(n+1) - A016172(n+1). (End)