A364204 Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1)).

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

Offset

1,7

Links

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

Formula

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

Mathematica

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

Crossrefs

Cf. A001817, A048272, A364011, A364205, A364232.

Sequence in context: A361685 A227193 A287397 * A111407 A374065 A084440

Adjacent sequences: A364201 A364202 A364203 * A364205 A364206 A364207

Keyword

sign

Author

Ilya Gutkovskiy, Jul 14 2023

Status

approved