A363978 - OEIS

%I #10 Jun 30 2023 15:35:35

%S 0,0,1,0,0,1,3,0,1,0,6,1,0,3,11,0,0,1,15,0,4,6,21,1,0,0,29,3,0,11,36,

%T 0,7,0,48,1,0,15,56,0,0,4,66,6,11,21,78,1,3,0,92,0,0,29,111,3,16,0,

%U 120,11,0,36,140,0,0,7,153,0,22,48,171,1,0,0,201,15,9,56,210,0,29,0,231,4,0,66,254,6,0

%N Expansion of Sum_{k>0} x^(3*k) / (1 - x^(4*k))^3.

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

%F a(n) = Sum_{d|n, d==3 mod 4} binomial((d+1)/4+1,2).

%t a[n_] := DivisorSum[n, Binomial[(#+1)/4+1,2] &, Mod[#, 4] == 3 &]; Array[a, 100] (* _Amiram Eldar_, Jun 30 2023 *)

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

%Y Cf. A363973.

%K nonn

%O 1,7

%A _Seiichi Manyama_, Jun 30 2023