A363977 Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^3.

1, 1, 1, 1, 4, 1, 1, 1, 7, 4, 1, 1, 11, 1, 4, 1, 16, 7, 1, 4, 22, 1, 1, 1, 32, 11, 7, 1, 37, 4, 1, 1, 46, 16, 4, 7, 56, 1, 11, 4, 67, 22, 1, 1, 88, 1, 1, 1, 92, 32, 16, 11, 106, 7, 4, 1, 121, 37, 1, 4, 137, 1, 28, 1, 167, 46, 1, 16, 172, 4, 1, 7, 191, 56, 32, 1, 211, 11, 1, 4, 238, 67, 1

Offset

1,5

Links

Table of n, a(n) for n=1..83.

Formula

G.f.: Sum_{k>0} k*(k+1)/2 * x^(4*k-3) / (1 - x^(4*k-3)).

a(n) = Sum_{d|n, d==1 mod 4} binomial((d+3)/4+1,2).

Mathematica

a[n_] := DivisorSum[n, Binomial[(#+3)/4+1, 2] &, Mod[#, 4] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 30 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%4==1)*binomial((d+3)/4+1, 2));

Crossrefs

Cf. A001826, A363903.

Cf. A363972.

Sequence in context: A182665 A131299 A360911 * A073937 A074058 A308552

Adjacent sequences: A363974 A363975 A363976 * A363978 A363979 A363980

Keyword

nonn

Author

Seiichi Manyama, Jun 30 2023

Status

approved