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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =6a(7) =10a(8) =20a(9) =36a(10) =72a(11) =136a(12) =273a(13) =532a(14) =1074a(15) =2137a(16) =4342a(17) =8766a(18) =17925a(19) =36574a(20) =75234a(21) =154749a(22) =320038a(23) =662490a(24) =1376653a(25) =2864534a(26) =5977603a(27) =12492157a(28) =26165052a(29) =54882573