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

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =18a(5) =38a(6) =81a(7) =171a(8) =366a(9) =787a(10) =1693a(11) =3661a(12) =7938a(13) =17240a(14) =37540a(15) =81892a(16) =178907a(17) =391483a(18) =857769a(19) =1881618a(20) =4132225a(21) =9083823a(22) =19986954a(23) =44014447a(24) =97002134a(25) =213933655a(26) =472137851a(27) =1042626752a(28) =2303780392a(29) =5093189194