Number of UDUD's in all Dyck paths of semilength n with no UUU's and no DDD's (U=(1,1), D=(1,-1)).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =9a(5) =24a(6) =63a(7) =164a(8) =423a(9) =1088a(10) =2794a(11) =7168a(12) =18385a(13) =47158a(14) =120991a(15) =310537a(16) =797381a(17) =2048456a(18) =5265059a(19) =13539331a(20) =34834238a(21) =89665630a(22) =230913976a(23) =594938458a(24) =1533501169a(25) =3954384384a(26) =10201142803a(27) =26326101399a(28) =67964928779a(29) =175524139820