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%I #6 Jul 09 2019 13:30:07
%S 1,1,1,0,1,0,0,-1,1,1,0,-1,0,0,-1,-1,1,2,1,0,0,-1,-1,-1,0,1,0,0,-1,-1,
%T -1,0,1,2,2,1,1,-1,0,-1,0,0,-1,-1,-1,0,-1,0,0,1,1,1,0,-1,0,0,-1,-1,-1,
%U 0,-1,0,0,1,1,1,2,1,2,0,1,-1,1,0,-1,-2,0,1,-1,-1,0,1,0,0,-1,-1,-1,0,-1,0,0,1,-1,-1,0,1,0,0,1,1,1,0,1,0,0,-1,-1,-1,0,1
%N Expansion of Product_{k>=0} (1 + x^(2^k) - x^(3*2^k)).
%F G.f. A(x) satisfies: A(x) = (1 + x - x^3) * A(x^2).
%F a(0) = a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n) - a(n-1).
%t nmax = 109; CoefficientList[Series[Product[(1 + x^(2^k) - x^(3 2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t nmax = 109; A[_] = 1; Do[A[x_] = (1 + x - x^3) A[x^2] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 1)/2] - a[(n - 3)/2]]; Table[a[n], {n, 0, 109}]
%Y Cf. A002487, A005590, A120562.
%K sign
%O 0,18
%A _Ilya Gutkovskiy_, Jul 09 2019
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