Number of Motzkin paths of length n having no consecutive (1,0) steps.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =11a(6) =25a(7) =55a(8) =129a(9) =303a(10) =721a(11) =1743a(12) =4241a(13) =10415a(14) =25761a(15) =64095a(16) =160385a(17) =403263a(18) =1018369a(19) =2581887a(20) =6569089a(21) =16767871a(22) =42927105a(23) =110194175a(24) =283574017a(25) =731427583a(26) =1890600193a(27) =4896499455a(28) =12704869633a(29) =33021750015