A363975 Expansion of Sum_{k>0} x^k / (1 - x^(3*k))^3.

1, 1, 1, 4, 1, 1, 7, 4, 1, 11, 1, 4, 16, 7, 1, 25, 1, 1, 29, 14, 7, 37, 1, 4, 46, 16, 1, 65, 1, 11, 67, 25, 1, 79, 7, 4, 92, 29, 16, 119, 1, 7, 121, 40, 1, 137, 1, 25, 160, 56, 1, 190, 1, 1, 191, 65, 29, 211, 1, 14, 232, 67, 7, 278, 16, 37, 277, 82, 1, 317, 1, 4, 326, 92, 46, 383, 7, 16, 379

Offset

1,4

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001817, A363901.

Cf. A363970.

Sequence in context: A046554 A010321 A046550 * A355777 A223489 A016521

Adjacent sequences: A363972 A363973 A363974 * A363976 A363977 A363978

Keyword

nonn

Author

Seiichi Manyama, Jun 30 2023

Status

approved