Number of Motzkin paths of length n with no level steps at height 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =11a(6) =23a(7) =48a(8) =107a(9) =244a(10) =578a(11) =1402a(12) =3485a(13) =8826a(14) =22729a(15) =59340a(16) =156766a(17) =418319a(18) =1125956a(19) =3053400a(20) =8334578a(21) =22881070a(22) =63135802a(23) =175000959a(24) =487042069a(25) =1360440914a(26) =3812681435a(27) =10717405374a(28) =30209571942a(29) =85368323429