A363259 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(4*k-1)).

0, 1, 0, 2, 1, 3, 0, 5, 0, 5, 3, 6, 0, 8, 0, 8, 4, 11, 0, 11, 0, 11, 5, 12, 2, 14, 0, 17, 6, 15, 0, 19, 0, 17, 7, 18, 0, 24, 5, 20, 8, 21, 0, 23, 0, 25, 9, 29, 0, 29, 0, 26, 16, 27, 0, 29, 0, 35, 11, 32, 3, 32, 0, 32, 12, 33, 7, 46, 0, 35, 13, 39, 0, 40, 0, 38, 14, 47, 0, 41, 8, 41, 22, 42, 0, 49, 0

Offset

1,4

Links

Table of n, a(n) for n=1..87.

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A364084, A364085.

Cf. A363392.

Sequence in context: A127474 A364015 A363158 * A326400 A281617 A280544

Adjacent sequences: A363256 A363257 A363258 * A363260 A363261 A363262

Keyword

nonn

Author

Seiichi Manyama, Jul 08 2023

Status

approved