Number of Dyck paths of semilength n having no ascents of length 4.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =37a(6) =111a(7) =345a(8) =1104a(9) =3611a(10) =12016a(11) =40548a(12) =138414a(13) =477076a(14) =1657956a(15) =5802920a(16) =20436910a(17) =72369903a(18) =257518806a(19) =920333307a(20) =3302003826a(21) =11888979066a(22) =42944410207a(23) =155576009845a(24) =565127618392