Number of Motzkin paths of length n avoiding UHHD.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =18a(6) =33a(7) =73a(8) =127a(9) =279a(10) =473a(11) =1045a(12) =1749a(13) =3905a(14) =6490a(15) =14652a(16) =24244a(17) =55286a(18) =91190a(19) =209748a(20) =345102a(21) =799580a(22) =1312844a(23) =3060614a(24) =5016396a(25) =11756454a(26) =19239412a(27) =45294870a(28) =74024768a(29) =174964546