Number of Dyck paths of semilength n such that each level has exactly three peaks or no peaks.

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =1a(5) =3a(6) =4a(7) =10a(8) =36a(9) =83a(10) =225a(11) =573a(12) =1444a(13) =3996a(14) =11840a(15) =34057a(16) =95573a(17) =267643a(18) =754744a(19) =2167250a(20) =6347944a(21) =18754719a(22) =55183269a(23) =161366349a(24) =471263668a(25) =1382569548a(26) =4085677052a(27) =12145287569a(28) =36193473369a(29) =107824201547