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%I #13 Jul 29 2023 10:35:51
%S 0,1,0,-2,1,3,0,-3,0,3,1,-6,0,8,3,-10,1,9,0,-13,0,9,1,-9,5,14,0,-16,1,
%T 9,0,-19,3,15,8,-18,0,20,0,-25,1,24,0,-25,9,21,1,-30,0,16,3,-28,1,27,
%U 16,-24,0,27,1,-39,0,32,0,-42,14,27,0,-37,3,24,1,-27,0,38,15,-40,8,42,0,-69
%N Expansion of Sum_{k>=0} x^(3*k+2) / (1 + x^(3*k+2))^2.
%H Seiichi Manyama, <a href="/A364235/b364235.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n, n/d==2 (mod 3)} (-1)^(d+1) * d.
%t nmax = 80; CoefficientList[Series[Sum[x^(3 k + 2)/(1 + x^(3 k + 2))^2, {k, 0, nmax}], {x, 0, nmax}], x] // Rest
%t Table[DivisorSum[n, (-1)^(# + 1) # &, MemberQ[{2}, Mod[n/#, 3]] &], {n, 1, 80}]
%Y Cf. A002129, A186690, A326400, A364015, A364205, A364232.
%K sign
%O 1,4
%A _Ilya Gutkovskiy_, Jul 14 2023
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