A364204 Expansion of Sum_{k>=0} x^(3*k+1) / (1 + x^(3*k+1)).
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, 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, -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
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
nmax = 92; CoefficientList[Series[Sum[x^(3 k + 1)/(1 + x^(3 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest Table[DivisorSum[n, (-1)^(# + 1) &, MemberQ[{1}, Mod[n/#, 3]] &], {n, 1, 92}]
Formula
a(n) = Sum_{d|n, n/d==1 (mod 3)} (-1)^(d+1).