login
A363904
Expansion of Sum_{k>0} x^(3*k) / (1 - x^(4*k))^2.
3
0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 1, 0, 2, 5, 0, 0, 1, 5, 0, 3, 3, 6, 1, 0, 0, 8, 2, 0, 5, 8, 0, 4, 0, 11, 1, 0, 5, 11, 0, 0, 3, 11, 3, 5, 6, 12, 1, 2, 0, 14, 0, 0, 8, 17, 2, 6, 0, 15, 5, 0, 8, 19, 0, 0, 4, 17, 0, 7, 11, 18, 1, 0, 0, 24, 5, 5, 11, 20, 0, 8, 0, 21, 3, 0, 11, 23, 3, 0, 5, 25, 6
OFFSET
1,7
LINKS
FORMULA
a(n) = (1/4) * Sum_{d|n, d==3 mod 4} (d+1) = (A001842(n) + A050452(n))/4.
G.f.: Sum_{k>0} k * x^(4*k-1) / (1 - x^(4*k-1)).
MATHEMATICA
a[n_] := DivisorSum[n, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d%4==3)*(d+1))/4;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 27 2023
STATUS
approved