A016162 Expansion of 1/((1-5*x)*(1-8*x)).

1, 13, 129, 1157, 9881, 82173, 673009, 5462197, 44088201, 354658733, 2847035489, 22825112037, 182845036921, 1463980998493, 11717951503569, 93774129606677, 750345624744041, 6003527937405453, 48032038196509249

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 (13,-40).

Crossrefs

Cf. A016161.

Programs

Magma

[n le 2 select 13^(n-1) else 13*Self(n-1) -40*Self(n-2): n in [1..31]]; // G. C. Greubel, Nov 09 2024

Mathematica

Table[(8^(n+1)-5^(n+1))/3, {n,0,30}] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1/((1-5x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[ {13,-40},{1,13},30] (* Harvey P. Dale, Feb 02 2015 *)

PARI

Vec(1/((1-5*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

SageMath

A016162=BinaryRecurrenceSequence(13,-40,1,13)
[A016162(n) for n in range(31)] # G. C. Greubel, Nov 09 2024

Formula

a(n) = (8^(n+1) - 5^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005

a(0)=1, a(n) = 8*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011

a(0)=1, a(1)=13, a(n) = 13*a(n-1) - 40*a(n-2). - Harvey P. Dale, Feb 02 2015

E.g.f.: (1/3)*(-5*exp(5*x) + 8*exp(8*x)). - G. C. Greubel, Nov 09 2024