A373335 Expansion of Sum_{k>=1} x^k / (1 + x^k + x^(2*k) + x^(3*k) + x^(4*k)).

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

Offset: 1

Author

Seiichi Manyama, Jun 01 2024

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A002324, A048272, A373336.

Cf. A001876, A001877.

Programs

PARI

my(N=110, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1-x^(5*k))))

PARI

a(n) = sumdiv(n, d, (d%5==1)-(d%5==2));

Formula

G.f.: Sum_{k>=1} x^k * (1 - x^k) / (1 - x^(5*k)).

a(n) = A001876(n) - A001877(n).