Generalized Motzkin paths with no hills and 3-horizontal steps.

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =3a(7) =5a(8) =9a(9) =17a(10) =34a(11) =64a(12) =128a(13) =251a(14) =505a(15) =1007a(16) =2044a(17) =4132a(18) =8444a(19) =17243a(20) =35461a(21) =72975a(22) =150910a(23) =312488a(24) =649359a(25) =1351478a(26) =2820366a(27) =5895019a(28) =12348082a(29) =25903960