%I #5 Jun 05 2021 16:44:51
%S 1,-1,-1,-2,1,1,0,1,1,-1,2,2,3,-1,-1,0,-1,-1,-1,0,0,1,-1,-1,0,-1,-1,
%T -2,1,1,3,-2,-2,0,-2,-2,1,-3,-3,-4,1,1,0,1,1,1,0,0,-1,1,1,0,1,1,0,1,1,
%U 1,0,0,0,0,0,1,-1,-1,-2,1,1,0,1,1,1,0,0,-1,1,1,0,1,1,-1,2,2,3,-1,-1,0,-1,-1,2,-3,-3,-5,2,2
%N a(0) = 1; a(3*n) = a(n) - a(n-1), a(3*n+1) = a(3*n+2) = -a(n).
%F G.f. A(x) satisfies: A(x) = (1 - x - x^2 - x^3) * A(x^3).
%F G.f.: Product_{k>=0} (1 - x^(3^k) - x^(2*3^k) - x^(3^(k+1))).
%t a[0] = 1; a[n_] := Switch[Mod[n, 3], 0, a[n/3] - a[(n - 3)/3], 1, -a[(n - 1)/3], 2, -a[(n - 2)/3]]; Table[a[n], {n, 0, 95}]
%t nmax = 95; A[_] = 1; Do[A[x_] = (1 - x - x^2 - x^3) A[x^3] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t nmax = 95; CoefficientList[Series[Product[(1 - x^(3^k) - x^(2 3^k) - x^(3^(k + 1))), {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]
%Y Cf. A054390, A177219, A309048, A345006.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Jun 05 2021
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