Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 3).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =6a(6) =16a(7) =37a(8) =83a(9) =199a(10) =512a(11) =1343a(12) =3488a(13) =9011a(14) =23488a(15) =62094a(16) =165738a(17) =444160a(18) =1193146a(19) =3216436a(20) =8709766a(21) =23683846a(22) =64611879a(23) =176730460a(24) =484593740a(25) =1332018207a(26) =3669981318a(27) =10133197561a(28) =28032766982a(29) =77688769031