A364011 - OEIS

A364011

Expansion of Sum_{k>0} x^k / (1 + x^(3*k)).

1, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 2, 2, 1, -1, 1, 1, 2, -1, 2, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, -1, 1, 0, 2, 0, 2, 2, 2, -2, 1, 2, 2, -1, 1, 0, 1, -1, 3, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, -1, 2, 2, 2, -2, 2, 0, 2, -1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, -3, 1, 0, 1, 0, 2, 2, 1, -2, 1, 0, 4, -1, 2, 0

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OFFSET

1,7

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: Sum_{k>0} (-1)^(k-1) * x^(3*k-2) / (1 - x^(3*k-2)).

a(n) = -Sum_{d|n, n/d==1 (mod 3)} (-1)^(n/d) = -Sum_{d|n, d==1 (mod 3)} (-1)^d.

MATHEMATICA

a[n_] := -DivisorSum[n, (-1)^(n/#) &, Mod[n/#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 01 2023 *)

PROG

(PARI) a(n) = -sumdiv(n, d, (d%3==1)*(-1)^d);