Number of equivalence classes of Dyck paths of semilength n for the string uuu.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =17a(7) =37a(8) =81a(9) =180a(10) =405a(11) =917a(12) =2090a(13) =4795a(14) =11054a(15) =25589a(16) =59475a(17) =138712a(18) =324483a(19) =761163a(20) =1790028a(21) =4219139a(22) =9965328a(23) =23582735a(24) =55906518a(25) =132751359a(26) =315700152a(27) =751837207a(28) =1792853416a(29) =4280568845