A374080 Expansion of Product_{k>=1} (1 - x^(4*k-1)) * (1 - x^(4*k)).
1, 0, 0, -1, -1, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, -1, 0, 1, 0, -1, -1, 0, 0, -1, -1, 1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 1, -1, -1, 1, 1, 0, 0, 1, 2, -1, -1, 0, 1, 0, -2, 0, 2, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -2, 0, 1, -1, -2, 1, 2, 0, -2, -1, 2, 0, -2
Offset: 0
Keywords
Links
- Ilya Gutkovskiy, Scatterplot of a(n) up to n=10000
Crossrefs
Programs
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Mathematica
nmax = 85; CoefficientList[Series[Product[(1 - x^(4 k - 1)) (1 - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] a[0] = 1; a[n_] := a[n] = -(1/n) Sum[DivisorSum[k, # &, Or[Mod[#, 4] == 0, Mod[#, 4] == 3] &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 85}]