a(n) = a(n-1) + Sum_{k=0..n-4} a(k)*a(n-4-k), a(0) = 1. Generalized Catalan Numbers.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =4a(6) =7a(7) =11a(8) =18a(9) =32a(10) =59a(11) =107a(12) =191a(13) =343a(14) =627a(15) =1159a(16) =2146a(17) =3972a(18) =7373a(19) =13757a(20) =25781a(21) =48437a(22) =91165a(23) =171945a(24) =325096a(25) =616066a(26) =1169667a(27) =2224355a(28) =4236728a(29) =8082374