A363259 - OEIS

%I #14 Jul 08 2023 08:05:14

%S 0,1,0,2,1,3,0,5,0,5,3,6,0,8,0,8,4,11,0,11,0,11,5,12,2,14,0,17,6,15,0,

%T 19,0,17,7,18,0,24,5,20,8,21,0,23,0,25,9,29,0,29,0,26,16,27,0,29,0,35,

%U 11,32,3,32,0,32,12,33,7,46,0,35,13,39,0,40,0,38,14,47,0,41,8,41,22,42,0,49,0

%N Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(4*k-1)).

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

%F G.f.: Sum_{k>0} x^(3*k-1) / (1 - x^(4*k-2))^2.

%t a[n_] := DivisorSum[4*n - 2, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* _Amiram Eldar_, Jul 08 2023 *)

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

%Y Cf. A364084, A364085.

%Y Cf. A363392.

%K nonn

%O 1,4

%A _Seiichi Manyama_, Jul 08 2023