%I #19 Jul 02 2023 10:03:06
%S 0,1,0,2,-1,3,0,5,0,3,-1,6,0,8,-3,10,-1,9,0,7,0,9,-1,15,-5,14,0,16,-1,
%T 9,0,21,-3,15,-8,18,0,20,0,19,-1,24,0,19,-9,21,-1,30,0,16,-3,28,-1,27,
%U -16,40,0,27,-1,21,0,32,0,42,-14,27,0,31,-3,24,-1,45,0,38,-15,40,-8,42,0
%N Expansion of Sum_{k>0} k * x^(2*k) / (1 + x^(3*k)).
%H Seiichi Manyama, <a href="/A364015/b364015.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>0} (-1)^(k-1) * x^(3*k-1) / (1 - x^(3*k-1))^2.
%F a(n) = Sum_{d|n, n/d==2 (mod 3)} (-1)^(n/d) * d.
%t a[n_] := DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 3] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jul 01 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (n/d%3==2)*(-1)^(n/d)*d);
%Y Cf. A364014, A364016.
%K sign
%O 1,4
%A _Seiichi Manyama_, Jul 01 2023
|