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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =5a(6) =12a(7) =27a(8) =60a(9) =135a(10) =309a(11) =716a(12) =1673a(13) =3935a(14) =9311a(15) =22154a(16) =52977a(17) =127255a(18) =306913a(19) =742918a(20) =1804301a(21) =4395371a(22) =10737206a(23) =26296601a(24) =64555741a(25) =158825720a(26) =391551973a(27) =967118177a(28) =2392964346a(29) =5930752193