A016172 Expansion of 1/((1-6*x)*(1-9*x)).

1, 15, 171, 1755, 17091, 161595, 1501011, 13789035, 125780931, 1142106075, 10339420851, 93417584715, 842935044771, 7599476096955, 68473649036691, 616733026314795, 5553418346740611, 49997691780110235

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-54).

Crossrefs

Cf. A016129.

Programs

Magma

[n le 2 select 15^(n-1) else 15*Self(n-1) -54*Self(n-2): n in [1..31]]; // G. C. Greubel, Nov 10 2024

Mathematica

Table[(9^(n+1)-6^(n+1))/3, {n,0,30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1/((1-6x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-54},{1,15},30] (* Harvey P. Dale, Oct 07 2015 *)

PARI

Vec(1/((1-6*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

SageMath

A016172=BinaryRecurrenceSequence(15,-54,1,15)
[A016172(n) for n in range(31)] # G. C. Greubel, Nov 10 2024

Formula

a(n) = (9^(n+1) - 6^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005

a(0)=1, a(n) = 9*a(n-1) + 6^n. - Vincenzo Librandi, Feb 09 2011

a(0)=1, a(1)=15, a(n) = 15*a(n-1) - 54*a(n-2). - Vincenzo Librandi, Feb 09 2011

E.g.f.: 3*exp(9*x) - 2*exp(6*x). - G. C. Greubel, Nov 10 2024