Number of length n left factors of Dyck paths having no UDUD's; here U=(1,1) and D=(1,-1).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =8a(6) =15a(7) =25a(8) =46a(9) =79a(10) =147a(11) =256a(12) =477a(13) =841a(14) =1570a(15) =2791a(16) =5217a(17) =9336a(18) =17467a(19) =31421a(20) =58830a(21) =106279a(22) =199103a(23) =360960a(24) =676545a(25) =1230185a(26) =2306642a(27) =4204931a(28) =7887045a(29) =14409480