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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =4a(5) =7a(6) =15a(7) =26a(8) =50a(9) =102a(10) =196a(11) =392a(12) =800a(13) =1609a(14) =3290a(15) =6786a(16) =13973a(17) =28998a(18) =60469a(19) =126295a(20) =264945a(21) =557594a(22) =1176004a(23) =2487485a(24) =5274110a(25) =11204631a(26) =23854581a(27) =50881939a(28) =108715072a(29) =232671125