A364205 Expansion of Sum_{k>=0} x^(3*k+2) / (1 + x^(3*k+2)).

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

Offset: 1

Author

Ilya Gutkovskiy, Jul 14 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A001822, A048272, A364014, A364204, A364235.

Programs

Mathematica

nmax = 92; CoefficientList[Series[Sum[x^(3 k + 2)/(1 + x^(3 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (-1)^(# + 1) &, MemberQ[{2}, Mod[n/#, 3]] &], {n, 1, 92}]

Formula

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