Number of plateau-free Motzkin paths of length n.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =5a(5) =11a(6) =26a(7) =61a(8) =147a(9) =357a(10) =879a(11) =2183a(12) =5471a(13) =13811a(14) =35100a(15) =89724a(16) =230562a(17) =595237a(18) =1543191a(19) =4016038a(20) =10487553a(21) =27473602a(22) =72178312a(23) =190127740a(24) =502044221a(25) =1328667241a(26) =3523684572a(27) =9363119781a(28) =24924679832a(29) =66461841934