A364232 Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1))^2.

1, -2, 3, -3, 5, -6, 8, -10, 9, -9, 11, -9, 14, -16, 15, -19, 17, -18, 20, -17, 24, -21, 23, -30, 26, -28, 27, -24, 29, -27, 32, -42, 33, -33, 40, -27, 38, -40, 42, -53, 41, -48, 44, -35, 45, -45, 47, -57, 57, -47, 51, -42, 53, -54, 56, -80, 60, -57, 59, -51, 62, -64, 72, -83, 70, -63, 68, -53, 69, -72

Offset: 1

Author

Ilya Gutkovskiy, Jul 14 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A002129, A186690, A326399, A364012, A364204, A364235.

Programs

Mathematica

nmax = 70; CoefficientList[Series[Sum[x^(3 k + 1)/(1 + x^(3 k + 1))^2, {k, 0, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (-1)^(# + 1) # &, MemberQ[{1}, Mod[n/#, 3]] &], {n, 1, 70}]

Formula

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