Number of Motzkin paths of length n with no level steps at height 2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =46a(7) =106a(8) =248a(9) =584a(10) =1389a(11) =3329a(12) =8047a(13) =19607a(14) =48167a(15) =119287a(16) =297829a(17) =749632a(18) =1902044a(19) =4864553a(20) =12538933a(21) =32568528a(22) =85224251a(23) =224618900a(24) =596106393a(25) =1592429464a(26) =4280667705a(27) =11575188106a(28) =31474407317a(29) =86029586086