A364018 Expansion of Sum_{k>0} (-1)^(k-1) * x^(3*k-1) / (1 - x^(3*k-1))^3.

0, 1, 0, 3, -1, 6, 0, 11, 0, 12, -1, 21, 0, 29, -6, 39, -1, 45, 0, 46, 0, 63, -1, 84, -15, 92, 0, 108, -1, 99, 0, 147, -6, 150, -29, 171, 0, 191, 0, 192, -1, 237, 0, 244, -45, 273, -1, 321, 0, 271, -6, 354, -1, 378, -81, 445, 0, 432, -1, 393, 0, 497, 0, 567, -92, 540, 0, 586, -6, 537, -1, 711, 0, 704, -120, 744

Offset: 1

Author

Seiichi Manyama, Jul 01 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A364015, A364017.

Programs

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/#) * Binomial[#+1, 2] &, Mod[n/#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d%3==2)*(-1)^(n/d)*binomial(d+1, 2));

Formula

G.f.: Sum_{k>0} k*(k+1)/2 * x^(2*k) / (1 + x^(3*k)).

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