G.f.: 1/G(0) where G(k) = 1 + (-q)^(k+1) / (1 - (-q)^(k+1)/G(k+1) ).

Terms

a(0) =1a(1) =1a(2) =0a(3) =0a(4) =1a(5) =0a(6) =0a(7) =1a(8) =0a(9) =1a(10) =1a(11) =0a(12) =2a(13) =1a(14) =1a(15) =3a(16) =2a(17) =3a(18) =4a(19) =4a(20) =6a(21) =7a(22) =8a(23) =11a(24) =13a(25) =16a(26) =20a(27) =24a(28) =31a(29) =37