Number of 3-generalized 2-Motzkin paths of length n with no level steps H=(3,0) at even level.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =2a(5) =2a(6) =5a(7) =8a(8) =18a(9) =30a(10) =66a(11) =120a(12) =252a(13) =484a(14) =1005a(15) =1984a(16) =4110a(17) =8278a(18) =17150a(19) =35024a(20) =72748a(21) =150012a(22) =312642a(23) =649424a(24) =1358244a(25) =2837484a(26) =5954980a(27) =12497616a(28) =26313432a(29) =55434248