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

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

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (13,-40).

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

Mathematica

Join[{a=1, b=13}, Table[c=13*b-40*a; a=b; b=c, {n, 60}]] (* 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 *)

Prog

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

Crossrefs

Sequence in context: A147669 A076457 A227749 * A155623 A023061 A255495

Adjacent sequences: A016159 A016160 A016161 * A016163 A016164 A016165

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved