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

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =8a(6) =13a(7) =22a(8) =37a(9) =64a(10) =111a(11) =195a(12) =346a(13) =618a(14) =1114a(15) =2019a(16) =3683a(17) =6753a(18) =12440a(19) =23018a(20) =42750a(21) =79683a(22) =148993a(23) =279407a(24) =525382a(25) =990325a(26) =1870993a(27) =3542241a(28) =6719450a(29) =12769653