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%I #8 Aug 13 2019 13:18:37
%S 1,1,3,5,12,20,42,74,148,264,506,918,1730,3154,5876,10760,19938,36574,
%T 67536,124048,228664,420248,773878,1422790,2618646,4815314,8859904,
%U 16293864,29974958,55128726,101408308,186511992,343068964,630989264,1160606794,2134665022
%N G.f. A(x) satisfies: A(x) = A(x^2) / (1 - x - x^2 - x^3).
%F G.f.: Product_{k>=0} 1/(1 - x^(2^k) - x^(2^(k+1)) - x^(3*2^k)).
%t nmax = 35; A[_] = 1; Do[A[x_] = A[x^2]/(1 - x - x^2 - x^3) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t nmax = 35; CoefficientList[Series[Product[1/(1 - x^(2^k) - x^(2^(k + 1)) - x^(3 2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%Y Cf. A000073, A018819, A173285, A309703.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 13 2019
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