Number of 2-Motzkin paths with no level steps at height 1.

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =30a(5) =76a(6) =197a(7) =522a(8) =1418a(9) =3956a(10) =11354a(11) =33554a(12) =102104a(13) =319608a(14) =1027237a(15) =3381714a(16) =11371366a(17) =38946892a(18) =135505958a(19) =477781296a(20) =1703671604a(21) =6132978608a(22) =22256615602a(23) =81327116484a(24) =298938112816