A164118 Expansion of (1 - x^2) * (1 - x^4) * (1 - x^5) / ((1 - x) * (1 - x^10)) in powers of x.

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

Offset: 0

Author

Michael Somos, Aug 10 2009

Keywords

• sign
• easy

Links

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

Crossrefs

A164116(n) = (-1)^n * a(n). Convolution inverse of A164117.

Programs

Mathematica

CoefficientList[Series[(1 - x^4) / (1 - x + x^2 - x^3 + x^4), {x, 0, 50}], x] (* G. C. Greubel, Sep 12 2017 *)

PARI

{a(n) = -(n==0) + [2, 1, 0, 0, -1, -2, -1, 0, 0, 1][n%10 + 1]}

Formula

Euler transform of length 10 sequence [ 1, -1, 0, -1, -1, 0, 0, 0, 0, 1].

a(-n) = a(n). a(n + 5) = -a(n) unless n=0 or n=-5.

G.f.: (1 - x^4) / (1 - x + x^2 - x^3 + x^4).