A363158 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k-2)).

0, 1, 0, 2, 1, 3, 0, 5, 0, 5, 1, 8, 0, 8, 0, 8, 1, 9, 3, 13, 0, 11, 1, 12, 0, 18, 0, 16, 1, 15, 0, 20, 5, 17, 1, 20, 0, 20, 0, 26, 1, 21, 0, 29, 3, 23, 8, 24, 0, 26, 0, 28, 1, 35, 0, 34, 0, 32, 1, 32, 9, 36, 0, 32, 1, 33, 0, 53, 0, 35, 4, 36, 0, 38, 11, 40, 1, 39, 5, 52, 0, 53, 1, 47, 0, 44, 0

Offset

1,4

Links

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

Formula

a(n) = (1/5) * Sum_{d | 5*n-4, d==3 (mod 5)} (d+2).

G.f.: Sum_{k>0} x^(3*k-1) / (1 - x^(5*k-3))^2.

Mathematica

a[n_] := DivisorSum[5*n - 4, # + 2 &, Mod[#, 5] == 3 &]/5; Array[a, 100] (* Amiram Eldar, Jul 06 2023 *)

Prog

(PARI) a(n) = sumdiv(5*n-4, d, (d%5==3)*(d+2))/5;

Crossrefs

Cf. A359244, A363053.

Sequence in context: A180988 A127474 A364015 * A363259 A326400 A281617

Adjacent sequences: A363155 A363156 A363157 * A363159 A363160 A363161

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2023

Status

approved