Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD and HH.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =2a(5) =2a(6) =5a(7) =10a(8) =16a(9) =34a(10) =68a(11) =128a(12) =264a(13) =536a(14) =1073a(15) =2217a(16) =4569a(17) =9404a(18) =19594a(19) =40875a(20) =85420a(21) =179525a(22) =378069a(23) =797935a(24) =1689550a(25) =3584560a(26) =7620071a(27) =16234510a(28) =34647429a(29) =74067643