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

Terms

a(0) =1a(1) =2a(2) =4a(3) =10a(4) =23a(5) =54a(6) =129a(7) =307a(8) =733a(9) =1757a(10) =4213a(11) =10115a(12) =24315a(13) =58481a(14) =140741a(15) =338890a(16) =816304a(17) =1966929a(18) =4740758a(19) =11428851a(20) =27557585a(21) =66458601a(22) =160295262a(23) =386671056a(24) =932839439a(25) =2250660384a(26) =5430575647a(27) =13104191607a(28) =31622724351a(29) =76314992880