G.f. satisfies A(x) = f(x)^2 + x*A(x)*f(x)^3, where f(x) = Sum_{k>=0} x^((4^k-1)/3).

Terms

a(0) =1a(1) =3a(2) =7a(3) =19a(4) =50a(5) =133a(6) =352a(7) =935a(8) =2482a(9) =6584a(10) =17473a(11) =46365a(12) =123034a(13) =326478a(14) =866338a(15) =2298895a(16) =6100296a(17) =16187616a(18) =42955106a(19) =113984740a(20) =302467434a(21) =802621041a(22) =2129817812a(23) =5651638433a(24) =14997065388a(25) =39795888008a(26) =105601506802