Number of Dyck paths of semilength n such that neighboring peaks have different heights.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =6a(5) =16a(6) =43a(7) =116a(8) =329a(9) =947a(10) =2762a(11) =8176a(12) =24469a(13) =73896a(14) =224960a(15) =689623a(16) =2126947a(17) =6595273a(18) =20548732a(19) =64298032a(20) =201969823a(21) =636639087a(22) =2013174695a(23) =6384574754a(24) =20302081620a(25) =64716553655a(26) =206764068578a(27) =661983640080