A363976 - OEIS

%I #9 Jun 30 2023 15:35:54

%S 0,1,0,1,3,1,0,7,0,4,10,1,0,16,3,7,21,1,0,32,0,11,36,7,3,46,0,16,55,4,

%T 0,73,10,22,81,1,0,92,0,38,105,16,0,131,3,37,136,7,0,157,21,46,171,1,

%U 13,212,0,56,210,32,0,232,0,73,256,11,0,298,36,97,300,7,0,326,3,92,361,46,0

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

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

%F a(n) = Sum_{d|n, d==2 mod 3} binomial((d+1)/3+1,2).

%t a[n_] := DivisorSum[n, Binomial[(#+1)/3+1,2] &, Mod[#, 3] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *)

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

%Y Cf. A363971.

%K nonn

%O 1,5

%A _Seiichi Manyama_, Jun 30 2023