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

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =2a(5) =2a(6) =4a(7) =8a(8) =12a(9) =21a(10) =40a(11) =69a(12) =122a(13) =227a(14) =412a(15) =747a(16) =1386a(17) =2567a(18) =4744a(19) =8851a(20) =16566a(21) =31004a(22) =58268a(23) =109858a(24) =207368a(25) =392331a(26) =744072a(27) =1413291a(28) =2688822a(29) =5124738