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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =3a(6) =4a(7) =6a(8) =10a(9) =16a(10) =28a(11) =48a(12) =85a(13) =152a(14) =273a(15) =497a(16) =906a(17) =1665a(18) =3071a(19) =5688a(20) =10579a(21) =19733a(22) =36934a(23) =69311a(24) =130415a(25) =245976a(26) =464944a(27) =880669a(28) =1671249a(29) =3177210