A111915 Expansion of -x^2*(x-1)*(x^2-x+1)*(x+x^2+1)/(1-x^4+x^8).

0, 0, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1, -2, 2, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1, -2, 2, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1, -2, 2, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1, -2, 2, -1, 1, -1, 1, 0, 0, 1, -1

Offset: 0

Author

Creighton Dement, Aug 20 2005

Keywords

• easy
• less
• sign

Comments

It appears that a(n) has period 24.

This is true, as (1-x^4+x^8) is the cyclotomic polynomial for n=24. - Joerg Arndt, Feb 03 2017

Links

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

Crossrefs

Cf. A085846, A111912, A111913, A111914.

Programs

Mathematica

CoefficientList[Series[-x^2*(x - 1)*(x^2 - x + 1)*(x + x^2 + 1)/(1 - x^4 + x^8), {x, 0, 100}], x] (* Wesley Ivan Hurt, Feb 03 2017 *)

PARI

a(n)=[0, 0, 1, -1, 1, -1, 2, -2, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1, -2, 2, -1, 1, -1, 1][n%24+1] \\ Charles R Greathouse IV, Feb 03 2017

Formula

G.f.: -x^2*(x-1)*(x^2-x+1)*(x+x^2+1)/(1-x^4+x^8).