Number of Dyck n-paths with ascents and descents of length equal to 1 (mod 3).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =4a(6) =7a(7) =12a(8) =22a(9) =42a(10) =80a(11) =152a(12) =292a(13) =568a(14) =1112a(15) =2185a(16) =4313a(17) =8557a(18) =17050a(19) =34089a(20) =68370a(21) =137542a(22) =277475a(23) =561185a(24) =1137595a(25) =2311014a(26) =4704235a(27) =9593662a(28) =19598920a(29) =40103635