A106804 Expansion of g.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).

0, 2, 11, 56, 285, 1452, 7406, 37816, 193295, 989002, 5065051, 25963276, 133199780, 683904902, 3514119571, 18069536436, 92975574865, 478701242652, 2466137174466, 12711910214796, 65558648361175, 338267429484502

Offset: 0

Author

Roger L. Bagula, May 30 2005

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 (10,-25,0,1).

Crossrefs

Cf. A004254, A052918.

Programs

Magma

I:=[0,2,11,56]; [n le 4 select I[n] else 10*Self(n-1) - 25*Self(n-2) + Self(n-4): n in [1..31]]; // G. C. Greubel, Sep 11 2021

Mathematica

M = {{0,0,0,1}, {1,5,0,0}, {0,1,0,0}, {0,0,1,5}}; v[1]= {0,1,1,2}; v[n_]:= v[n]= M.v[n-1]; Table[v[n][[1]], {n, 20}]
LinearRecurrence[{10,-25,0,1},{0,2,11,56},30] (* Harvey P. Dale, Nov 29 2018 *)

Sage

def A106804_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(2-9*x-4*x^2)/((1-5*x+x^2)*(1-5*x-x^2)) ).list()
A106804_list(30) # G. C. Greubel, Sep 11 2021

Formula

G.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).

a(n) = (1/2)*((A052918(n) - 2*A052918(n-1)) - (A004254(n+1) - 6*A004254(n))). - G. C. Greubel, Sep 11 2021

Extensions

Edited by the Associate Editors of the OEIS, Apr 09 2009

Mathematica code fixed by Olivier Gérard, Dec 13 2011