A364017 Expansion of Sum_{k>0} (-1)^(k-1) * x^(3*k-2) / (1 - x^(3*k-2))^3.

1, 3, 6, 9, 15, 21, 29, 33, 45, 54, 66, 72, 92, 108, 120, 125, 153, 171, 191, 192, 237, 252, 276, 279, 326, 354, 378, 387, 435, 459, 497, 489, 561, 594, 645, 621, 704, 744, 786, 754, 861, 924, 947, 921, 1035, 1080, 1128, 1092, 1254, 1263, 1326

Offset

1,2

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A364012, A364018.

Sequence in context: A007187 A337502 A082004 * A352733 A112773 A363615

Adjacent sequences: A364014 A364015 A364016 * A364018 A364019 A364020

Keyword

nonn

Author

Seiichi Manyama, Jul 01 2023

Status

approved