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

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =20a(7) =36a(8) =73a(9) =139a(10) =286a(11) =567a(12) =1182a(13) =2412a(14) =5085a(15) =10595a(16) =22551a(17) =47712a(18) =102384a(19) =219131a(20) =473523a(21) =1022557a(22) =2222985a(23) =4834578a(24) =10564962a(25) =23109481a(26) =50730082a(27) =111497080a(28) =245729655a(29) =542263213