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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =4a(5) =6a(6) =12a(7) =20a(8) =33a(9) =61a(10) =109a(11) =191a(12) =349a(13) =639a(14) =1159a(15) =2133a(16) =3953a(17) =7311a(18) =13595a(19) =25417a(20) =47570a(21) =89272a(22) =168126a(23) =317226a(24) =599699a(25) =1136403a(26) =2157363a(27) =4102113a(28) =7813560a(29) =14906230