A363976 Expansion of Sum_{k>0} x^(2*k) / (1 - x^(3*k))^3.

0, 1, 0, 1, 3, 1, 0, 7, 0, 4, 10, 1, 0, 16, 3, 7, 21, 1, 0, 32, 0, 11, 36, 7, 3, 46, 0, 16, 55, 4, 0, 73, 10, 22, 81, 1, 0, 92, 0, 38, 105, 16, 0, 131, 3, 37, 136, 7, 0, 157, 21, 46, 171, 1, 13, 212, 0, 56, 210, 32, 0, 232, 0, 73, 256, 11, 0, 298, 36, 97, 300, 7, 0, 326, 3, 92, 361, 46, 0

Offset

1,5

Links

Table of n, a(n) for n=1..79.

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, Binomial[(#+1)/3+1, 2] &, Mod[#, 3] == 2 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

Prog

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

Crossrefs

Cf. A363971.

Sequence in context: A058152 A058140 A074678 * A201586 A130888 A010601

Adjacent sequences: A363973 A363974 A363975 * A363977 A363978 A363979

Keyword

nonn

Author

Seiichi Manyama, Jun 30 2023

Status

approved