A081655 2*5^n-1.

1, 9, 49, 249, 1249, 6249, 31249, 156249, 781249, 3906249, 19531249, 97656249, 488281249, 2441406249, 12207031249, 61035156249, 305175781249, 1525878906249, 7629394531249, 38146972656249, 190734863281249

Offset: 0

Author

Paul Barry, Mar 26 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081654. Inverse binomial transform of A081656.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Programs

Magma

[2*5^n-1: n in [0..30]]; // Vincenzo Librandi, Aug 10 2013

Mathematica

CoefficientList[Series[(1 + 3 x) / ((1 - 5 x) (1 - x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)
NestList[5#+4&,1,30] (* Harvey P. Dale, Jul 04 2014 *)

PARI

a(n)=2*5^n-1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: (1+3*x)/((1-5*x)*(1-x)).

E.g.f. 2*exp(5*x)-exp(x).

a(n) = 5*a(n-1)+4, with a(0)=1. - Vincenzo Librandi, Aug 01 2010