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

Terms

a(0) =1a(1) =2a(2) =4a(3) =10a(4) =24a(5) =60a(6) =152a(7) =388a(8) =1000a(9) =2592a(10) =6752a(11) =17664a(12) =46368a(13) =122080a(14) =322240a(15) =852464a(16) =2259552a(17) =5999552a(18) =15954560a(19) =42486592a(20) =113282048a(21) =302386304a(22) =807999744a(23) =2161077120a(24) =5785032448a(25) =15498450944a(26) =41551965184a(27) =111478804480a(28) =299274439680a(29) =803905119232