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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =3a(5) =3a(6) =8a(7) =12a(8) =13a(9) =27a(10) =50a(11) =64a(12) =109a(13) =215a(14) =322a(15) =504a(16) =966a(17) =1616a(18) =2526a(19) =4578a(20) =8115a(21) =13143a(22) =22836a(23) =41162a(24) =69410a(25) =118536a(26) =212498a(27) =369226a(28) =631631a(29) =1119755