G.f.: 1/G(0) where G(k) = 1 - q^(k+1) / (1 - q^(k+2)/G(k+1) ).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =10a(7) =19a(8) =34a(9) =63a(10) =115a(11) =213a(12) =391a(13) =723a(14) =1333a(15) =2463a(16) =4547a(17) =8403a(18) =15522a(19) =28686a(20) =53006a(21) =97963a(22) =181042a(23) =334606a(24) =618415a(25) =1142994a(26) =2112545a(27) =3904592a(28) =7216810a(29) =13338856