A111912 Expansion of x*(2 +3*x +x^2 -2*x^5 -x^7 -x^8)/((1-x)*(1+x)*(1-x^4+x^8)).

0, 2, 3, 3, 3, 5, 4, 6, 3, 5, 1, 5, 0, 2, -3, 1, -3, -1, -4, -2, -3, -1, -1, -1, 0, 2, 3, 3, 3, 5, 4, 6, 3, 5, 1, 5, 0, 2, -3, 1, -3, -1, -4, -2, -3, -1, -1, -1, 0, 2, 3, 3, 3, 5, 4, 6, 3, 5, 1, 5, 0, 2, -3, 1, -3, -1, -4, -2, -3, -1, -1, -1

Offset: 0

Author

Creighton Dement, Aug 20 2005

Keywords

• sign
• easy
• less

Comments

Sequence has period 24.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1,0,-1,0,1).

Crossrefs

Cf. A085846, A111913, A111914, A111915.

Programs

Magma

R:=PowerSeriesRing(Integers(), 75);
Coefficients(R!( x*(2+3*x+x^2-2*x^5-x^7-x^8)/((1-x)*(1+x)*(1-x^4+x^8)) )); // G. C. Greubel, Feb 12 2021

Maple

seq(coeff(series((x*(-2-3*x-x^2+2*x^5+x^7+x^8)/((x-1)*(x+1)*(x^8-x^4+1))),x,n+1),x,n),n=0..75); # Muniru A Asiru, Jun 06 2018

Mathematica

LinearRecurrence[{0,1,0,1,0,-1,0,-1,0,1}, {0,2,3,3,3,5,4,6,3,5}, 75] (* G. C. Greubel, Feb 12 2021 *)

PARI

Vec(x*(-2-3*x-x^2+2*x^5+x^7+x^8)/((x-1)*(x+1)*(x^8-x^4+1))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

def A111912_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(2+3*x+x^2-2*x^5-x^7-x^8)/((1-x)*(1+x)*(1-x^4+x^8)) ).list()
A111912_list(75) # G. C. Greubel, Feb 12 2021