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

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =12a(5) =24a(6) =50a(7) =105a(8) =221a(9) =471a(10) =1008a(11) =2164a(12) =4669a(13) =10102a(14) =21909a(15) =47642a(16) =103801a(17) =226549a(18) =495284a(19) =1084318a(20) =2376902a(21) =5216543a(22) =11460725a(23) =25203497a(24) =55475172a(25) =122205631a(26) =269408827a(27) =594343482a(28) =1312035579a(29) =2898123874