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

0,2

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).

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

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 *)

Prog

(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
(Sage)
def A106804_list(prec):
    P.<x> = 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

Crossrefs

Cf. A004254, A052918.

Sequence in context: A212388 A198769 A037554 * A361219 A213098 A041129

Adjacent sequences: A106801 A106802 A106803 * A106805 A106806 A106807

Keyword

nonn,easy

Author

Roger L. Bagula, May 30 2005

Extensions

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

Mathematica code fixed by Olivier Gérard, Dec 13 2011

Status

approved