Number of Motzkin paths of length n having no UHD's (U=(1,1), H=(1,0), D=(1,-1)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =15a(6) =36a(7) =85a(8) =209a(9) =517a(10) =1303a(11) =3312a(12) =8510a(13) =22029a(14) =57447a(15) =150709a(16) =397569a(17) =1053822a(18) =2805518a(19) =7498035a(20) =20110254a(21) =54110386a(22) =146021880a(23) =395114304a(24) =1071772322a(25) =2913900196a(26) =7939004648a(27) =21672609566a(28) =59272260791a(29) =162380575451