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%I #14 Jul 29 2023 10:33:50
%S 1,-1,1,0,1,-1,2,-2,1,0,1,0,2,-2,1,-1,1,-1,2,-1,2,0,1,-2,2,-2,1,0,1,0,
%T 2,-3,1,0,2,0,2,-2,2,-2,1,-2,2,-1,1,0,1,-1,3,-1,1,0,1,-1,2,-4,2,0,1,
%U -1,2,-2,2,-2,2,0,2,-1,1,0,1,-2,2,-2,2,0,2,-2,2,-3,1,0,1,0,2,-2,1,-2,1,0,4,-1
%N Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1)).
%H Seiichi Manyama, <a href="/A364204/b364204.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n, n/d==1 (mod 3)} (-1)^(d+1).
%t nmax = 92; CoefficientList[Series[Sum[x^(3 k + 1)/(1 + x^(3 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest
%t Table[DivisorSum[n, (-1)^(# + 1) &, MemberQ[{1}, Mod[n/#, 3]] &], {n, 1, 92}]
%Y Cf. A001817, A048272, A364011, A364205, A364232.
%K sign
%O 1,7
%A _Ilya Gutkovskiy_, Jul 14 2023