A020579 Expansion of g.f. 1/((1-6*x)*(1-8*x)*(1-9*x)).

1, 23, 355, 4595, 53851, 592403, 6240235, 63710915, 635468251, 6225852083, 60146237515, 574587484835, 5439634923451, 51116555484563, 477406092913195, 4435981769620355, 41041272503703451, 378327871809737843, 3476703760455563275, 31864966517183461475, 291385416197758352251

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 (23,-174,432).

Crossrefs

Cf. A016170, A016172.

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-8*x)*(1-9*x)))); // Vincenzo Librandi, Jul 04 2013

Magma

I:=[1,23,355]; [n le 3 select I[n] else 23*Self(n-1)-174*Self(n-2)+432*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1 / ((1 - 6 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 04 2013 *)

Formula

a(n) = 6*6^n - 32*8^n + 27*9^n. - R. J. Mathar, Jun 30 2013

From Vincenzo Librandi, Jul 04 2013: (Start)

a(0)=1, a(1)=23, a(2)=355; for n>2, a(n) = 23*a(n-1) - 174*a(n-2) + 432*a(n-3).

a(n) = 17*a(n-1) - 72*a(n-2) + 6^n. (End)

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

E.g.f.: exp(6*x)*(6 - 32*exp(2*x) + 27*exp(3*x)).

a(n) = A016172(n+1) - A016170(n+1). (End)