A364014 Expansion of Sum_{k>0} x^(2*k) / (1 + x^(3*k)).

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

Offset

1,8

Links

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

Formula

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

a(n) = Sum_{d|n, n/d==2 (mod 3)} (-1)^(n/d) = Sum_{d|n, d==2 (mod 3)} (-1)^d.

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/#) &, Mod[n/#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%3==2)*(-1)^d);

Crossrefs

Cf. A364015, A364016.

Sequence in context: A147696 A001842 A216654 * A326016 A326033 A029429

Adjacent sequences: A364011 A364012 A364013 * A364015 A364016 A364017

Keyword

sign

Author

Seiichi Manyama, Jul 01 2023

Status

approved