Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =9a(7) =16a(8) =30a(9) =56a(10) =108a(11) =208a(12) =409a(13) =805a(14) =1606a(15) =3211a(16) =6479a(17) =13108a(18) =26691a(19) =54499a(20) =111808a(21) =229983a(22) =474787a(23) =982528a(24) =2039143a(25) =4241187a(26) =8842137a(27) =18469760a(28) =38657209a(29) =81047625