Number of Motzkin paths of length n with all ascents ending at odd heights.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =16a(6) =33a(7) =70a(8) =152a(9) =336a(10) =754a(11) =1714a(12) =3940a(13) =9144a(14) =21397a(15) =50428a(16) =119593a(17) =285190a(18) =683422a(19) =1644914a(20) =3974702a(21) =9638478a(22) =23448390a(23) =57213068a(24) =139974092a(25) =343301696a(26) =843911294a(27) =2078912816a(28) =5131312480a(29) =12688618168