A112523 Expansion of x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4) / ((1+4*x^2)*(1+x^2)*(1-x^2+x^4)).

0, 1, 3, -8, -17, 35, 72, -145, -291, 584, 1169, -2339, -4680, 9361, 18723, -37448, -74897, 149795, 299592, -599185, -1198371, 2396744, 4793489, -9586979, -19173960, 38347921, 76695843, -153391688, -306783377, 613566755, 1227133512, -2454267025, -4908534051, 9817068104

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,-4,0,0,0,-1,0,-4).

Formula

a(n) = -4*a(n-2) - a(n-6) - 4*a(n-8). - Colin Barker, May 18 2019

Mathematica

LinearRecurrence[{0, -4, 0, 0, 0, -1, 0, -4}, {0, 1, 3, -8, -17, 35, 72, -145, -291}, 40] (* G. C. Greubel, Jan 12 2022 *)

Prog

(PARI) my(x='x+O('x^40)); concat([0], Vec(x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4)/((1+4*x^2)*(1+x^2)*(1-x^2+x^4)))) \\ Charles R Greathouse IV, Sep 27 2012
(Sage)
def A112523_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4)/((1+4*x^2)*(1+x^2)*(1-x^2+x^4)) ).list()
A112523_list(40) # G. C. Greubel, Jan 12 2022
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
[0] cat Coefficients(R!( x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4)/((1+4*x^2)*(1+x^2)*(1-x^2+x^4)) )); // G. C. Greubel, Jan 12 2022

Crossrefs

Cf. A112522.

Sequence in context: A182616 A159217 A052996 * A369734 A147419 A106691

Adjacent sequences: A112520 A112521 A112522 * A112524 A112525 A112526

Keyword

sign,easy

Author

Creighton Dement, Sep 09 2005

Status

approved