A364013 Expansion of Sum_{k>0} k^2 * x^k / (1 + x^(3*k)).

1, 4, 9, 15, 25, 36, 50, 60, 81, 99, 121, 135, 170, 200, 225, 239, 289, 324, 362, 371, 450, 483, 529, 540, 626, 680, 729, 750, 841, 891, 962, 956, 1089, 1155, 1250, 1215, 1370, 1448, 1530, 1483, 1681, 1800, 1850, 1811, 2025, 2115, 2209, 2151, 2451, 2479, 2601, 2550, 2809, 2916, 3026

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

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

Mathematica

a[n_] := -DivisorSum[n, (-1)^(n/#) * #^2 &, Mod[n/#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 01 2023 *)

Prog

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

Crossrefs

Cf. A364011, A364012.

Cf. A050470.

Sequence in context: A030664 A070160 A244672 * A056928 A225283 A122964

Adjacent sequences: A364010 A364011 A364012 * A364014 A364015 A364016

Keyword

nonn

Author

Seiichi Manyama, Jul 01 2023

Status

approved