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

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =4a(5) =5a(6) =11a(7) =17a(8) =38a(9) =67a(10) =148a(11) =282a(12) =616a(13) =1231a(14) =2674a(15) =5511a(16) =11957a(17) =25162a(18) =54673a(19) =116748a(20) =254393a(21) =549035a(22) =1200429a(23) =2611594a(24) =5730385a(25) =12544520a(26) =27620602a(27) =60766999a(28) =134232576a(29) =296533559