A364235 Expansion of Sum_{k>=0} x^(3*k+2) / (1 + x^(3*k+2))^2.

0, 1, 0, -2, 1, 3, 0, -3, 0, 3, 1, -6, 0, 8, 3, -10, 1, 9, 0, -13, 0, 9, 1, -9, 5, 14, 0, -16, 1, 9, 0, -19, 3, 15, 8, -18, 0, 20, 0, -25, 1, 24, 0, -25, 9, 21, 1, -30, 0, 16, 3, -28, 1, 27, 16, -24, 0, 27, 1, -39, 0, 32, 0, -42, 14, 27, 0, -37, 3, 24, 1, -27, 0, 38, 15, -40, 8, 42, 0, -69

Offset

1,4

Links

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

Formula

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

Mathematica

nmax = 80; CoefficientList[Series[Sum[x^(3 k + 2)/(1 + x^(3 k + 2))^2, {k, 0, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (-1)^(# + 1) # &, MemberQ[{2}, Mod[n/#, 3]] &], {n, 1, 80}]

Crossrefs

Cf. A002129, A186690, A326400, A364015, A364205, A364232.

Sequence in context: A194665 A004563 A329647 * A146094 A098035 A079055

Adjacent sequences: A364232 A364233 A364234 * A364236 A364237 A364238

Keyword

sign

Author

Ilya Gutkovskiy, Jul 14 2023

Status

approved