Number of 3-Motzkin paths of length n with no level steps at even level.

Terms

a(0) =1a(1) =0a(2) =1a(3) =3a(4) =11a(5) =39a(6) =140a(7) =504a(8) =1823a(9) =6621a(10) =24144a(11) =88380a(12) =324699a(13) =1197045a(14) =4427565a(15) =16427385a(16) =61129025a(17) =228103185a(18) =853399640a(19) =3200710680a(20) =12032399045a(21) =45332769075a(22) =171148151095a(23) =647412581643