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

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =11a(5) =21a(6) =42a(7) =83a(8) =167a(9) =341a(10) =697a(11) =1437a(12) =2983a(13) =6211a(14) =12996a(15) =27304a(16) =57528a(17) =121601a(18) =257759a(19) =547652a(20) =1166299a(21) =2489010a(22) =5321780a(23) =11398972a(24) =24456235a(25) =52549847a(26) =113077188a(27) =243645011a(28) =525630690a(29) =1135309380