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A364067
Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(3*k-1)).
1
0, 1, 0, 3, 0, 4, 0, 5, 2, 6, 0, 7, 0, 13, 0, 9, 0, 10, 6, 11, 0, 15, 0, 20, 0, 14, 0, 15, 8, 23, 0, 17, 0, 27, 0, 19, 0, 28, 10, 21, 4, 22, 0, 34, 0, 33, 0, 25, 12, 26, 0, 36, 0, 51, 0, 29, 0, 30, 14, 31, 0, 43, 10, 48, 0, 39, 0, 35, 16, 48, 0, 37, 0, 66, 0, 39, 0, 53, 18, 52, 0, 42, 0, 62, 12, 58, 0, 45
OFFSET
1,4
LINKS
FORMULA
a(n) = (1/3) * Sum_{d | 3*n-2, d==2 (mod 3)} (d+1).
G.f.: Sum_{k>0} x^(2*k) / (1 - x^(3*k-1))^2.
MATHEMATICA
a[n_] := DivisorSum[3*n - 2, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)
PROG
(PARI) a(n) = sumdiv(3*n-2, d, (d%3==2)*(d+1))/3;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 04 2023
STATUS
approved