A363258 Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(4*k-3)).

1, 1, 3, 1, 4, 1, 5, 3, 6, 1, 7, 1, 10, 4, 9, 1, 10, 3, 11, 5, 12, 1, 18, 1, 14, 6, 15, 3, 16, 1, 17, 10, 24, 1, 19, 1, 20, 10, 21, 1, 25, 1, 30, 9, 24, 5, 25, 3, 26, 13, 27, 1, 36, 1, 29, 11, 30, 3, 38, 6, 32, 12, 42, 1, 34, 1, 35, 18, 36, 1, 37, 5, 48, 20, 39, 1, 48, 3, 41, 15, 42, 1, 54, 1, 48, 19, 45, 10

Offset

1,3

Links

Table of n, a(n) for n=1..88.

Formula

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

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

Mathematica

a[n_] := DivisorSum[4*n - 2, # + 3 &, Mod[#, 4] == 1 &]/4; Array[a, 100] (* Amiram Eldar, Jul 08 2023 *)

Prog

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

Crossrefs

Cf. A364082, A364083.

Cf. A363316.

Sequence in context: A259655 A221185 A242746 * A327642 A358919 A354617

Adjacent sequences: A363255 A363256 A363257 * A363259 A363260 A363261

Keyword

nonn

Author

Seiichi Manyama, Jul 08 2023

Status

approved