A113414 - OEIS

A113414

Expansion of Sum_{k>0} x^k/(1-(-x^2)^k).

1, 1, 0, 1, 2, 2, 0, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 3, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 2, 4, 0, 1, 0, 2, 0, 3, 2, 2, 0, 2, 2, 4, 0, 2, 2, 2, 0, 2, 1, 3, 0, 2, 2, 4, 0, 2, 0, 2, 0, 4, 2, 2, 0, 1, 4, 4, 0, 2, 0, 4, 0, 3, 2, 2, 0, 2, 0, 4, 0, 2, 1, 2, 0, 4, 4, 2, 0, 2, 2, 6, 0, 2, 0, 2, 0, 2, 2, 3, 0, 3, 2, 4, 0, 2, 0

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Moebius transform is period 8 sequence [1, 0, -1, 0, 1, 2, -1, 0, ...].

G.f.: Sum_{k>0} x^k/(1-(-x^2)^k) = Sum_{k>0} x^k/(1+x^(2k))+2x^(6k)/(1-x^(8k)) = Sum_{k>0} -(-1)^k x^(2k-1)/(1+(-1)^k*x^(2k-1)).

a(4n+3) = 0.

a(n) = A001826(n) + (-1)^n * A001842(n). - David Spies, Sep 26 2012

PROG

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-4, d)+2*(n%2==0)*(d%4==3)))