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

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =11a(5) =20a(6) =38a(7) =72a(8) =136a(9) =260a(10) =499a(11) =958a(12) =1847a(13) =3572a(14) =6917a(15) =13422a(16) =26097a(17) =50808a(18) =99049a(19) =193354a(20) =377857a(21) =739148a(22) =1447292a(23) =2836316a(24) =5562774a(25) =10918180a(26) =21444029a(27) =42143986a(28) =82874681a(29) =163060540