Number of Dyck paths of semilength n having no ascents of length 2.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =6a(5) =17a(6) =46a(7) =128a(8) =372a(9) =1109a(10) =3349a(11) =10221a(12) =31527a(13) =98178a(14) =308179a(15) =973911a(16) =3096044a(17) =9894393a(18) =31770247a(19) =102444145a(20) =331594081a(21) =1077022622a(22) =3509197080a(23) =11466710630a(24) =37567784437a(25) =123380796192a(26) =406120349756