a(n+1) = Sum_{k=0..floor(n/3)} a(k) * a(n-k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =5a(7) =10a(8) =18a(9) =33a(10) =66a(11) =127a(12) =244a(13) =506a(14) =1009a(15) =2018a(16) =4229a(17) =8631a(18) =17631a(19) =37265a(20) =77349a(21) =160433a(22) =342807a(23) =720334a(24) =1513791a(25) =3254445a(26) =6902283a(27) =14634519a(28) =31602375a(29) =67522598