Number of 3-Motzkin paths with no level steps at height 1.

Terms

a(0) =1a(1) =3a(2) =10a(3) =33a(4) =110a(5) =369a(6) =1247a(7) =4248a(8) =14603a(9) =50724a(10) =178314a(11) =635526a(12) =2300829a(13) =8477382a(14) =31842897a(15) =122103276a(16) =478372886a(17) =1915188093a(18) =7831613468a(19) =32674683984a(20) =138871668314a(21) =600140517762