A135138 a(n) = 5*a(n-2) + 2*a(n-3).

0, 0, 1, 0, 5, 2, 25, 20, 129, 150, 685, 1008, 3725, 6410, 20641, 39500, 116025, 238782, 659125, 1425960, 3773189, 8448050, 21717865, 49786628, 125485425, 292368870, 727000381, 1712815200, 4219739645, 10018076762, 24524328625, 58529863100

Offset: 0

Author

Paul Curtz, Feb 13 2008

Keywords

• nonn
• easy

Comments

a(n+2), n>=0, is the (5,2)-Padovan sequence p(5,2;n)with o.g.f. 1/(1-5*x^2-2*x^3). See A000931(n+3) ((1,1)-Padovan), and the W. Lang link given there, also for a combinatorial interpretation. - Wolfdieter Lang, Jun 28 2010

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,5,2).

Crossrefs

Cf. A135139.

Programs

Mathematica

a = {0, 0, 1}; Do[AppendTo[a, 5*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* Stefan Steinerberger, Feb 15 2008 *)
LinearRecurrence[{0, 5, 2}, {0, 0, 1}, 100] (* G. C. Greubel, Sep 28 2016 *)

Formula

From R. J. Mathar, Feb 15 2008: (Start)

O.g.f.: -x^2 / ( (2*x+1)*(x^2+2*x-1) ).

a(n) = [(-2)^n + A078343(n)]/7. (End)

Extensions

More terms from R. J. Mathar and Stefan Steinerberger, Feb 15 2008