Number of Dyck paths of semilength n having no ascents of length 3.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =27a(6) =79a(7) =240a(8) =750a(9) =2387a(10) =7711a(11) =25214a(12) =83315a(13) =277799a(14) =933596a(15) =3159187a(16) =10755190a(17) =36811479a(18) =126594819a(19) =437220744a(20) =1515844359a(21) =5273760446a(22) =18406122609a(23) =64426136558a(24) =226108087891a(25) =795486834627