%I #21 Jul 03 2023 01:00:16
%S 0,1,0,1,-1,1,0,2,0,0,-1,1,0,2,-1,2,-1,1,0,1,0,0,-1,2,-1,2,0,2,-1,0,0,
%T 3,-1,0,-2,1,0,2,0,2,-1,2,0,1,-1,0,-1,2,0,1,-1,2,-1,1,-2,4,0,0,-1,1,0,
%U 2,0,3,-2,0,0,1,-1,0,-1,2,0,2,-1,2,-2,2,0,3,0,0,-1,2,-2,2,-1,2,-1,0,0,1,0,0,-2,3,0
%N Expansion of Sum_{k>0} x^(2*k) / (1 + x^(3*k)).
%H Seiichi Manyama, <a href="/A364014/b364014.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)).
%F a(n) = Sum_{d|n, n/d==2 (mod 3)} (-1)^(n/d) = Sum_{d|n, d==2 (mod 3)} (-1)^d.
%t a[n_] := DivisorSum[n, (-1)^(n/#) &, Mod[n/#, 3] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (d%3==2)*(-1)^d);
%Y Cf. A364015, A364016.
%K sign
%O 1,8
%A _Seiichi Manyama_, Jul 01 2023