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A374060 Expansion of Product_{k>=1} (1 - x^(3*k-1)) * (1 - x^(3*k)).

%I A374060 #6 Jun 27 2024 06:27:00
%S A374060 1,0,-1,-1,0,0,-1,1,1,0,0,1,0,0,1,0,-1,0,0,-1,0,1,-1,-1,0,-1,0,1,0,-1,
%T A374060 1,0,-1,1,1,-1,0,1,0,1,1,-1,0,1,-1,-1,2,0,-1,1,0,-1,1,0,-2,0,0,-1,1,1,
%U A374060 -2,0,1,-2,0,2,-1,-1,1,-1,-1,2,-1,-1,2,0,-1,2,1,-2,1,0,-2,2,1,-2
%N A374060 Expansion of Product_{k>=1} (1 - x^(3*k-1)) * (1 - x^(3*k)).
%H A374060 Ilya Gutkovskiy, <a href="/A374060/a374060.jpg">Scatterplot of a(n) up to n=10000</a>
%F A374060 a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A082050(k) * a(n-k).
%F A374060 a(0) = 1; a(n) = -Sum_{k=1..n} A035361(k) * a(n-k).
%F A374060 a(n) = Sum_{k=0..n} A010815(k) * A035382(n-k).
%t A374060 nmax = 85; CoefficientList[Series[Product[(1 - x^(3 k - 1)) (1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A374060 a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Plus @@ Select[Divisors[k], Mod[#, 3] != 1 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 85}]
%Y A374060 Cf. A010815, A035361, A035382, A081362, A082050, A132462, A137569, A274719, A284315, A374058.
%K A374060 sign
%O A374060 0,47
%A A374060 _Ilya Gutkovskiy_, Jun 27 2024