Number of 3-Motzkin paths of length n with no level steps at odd level.

Terms

a(0) =1a(1) =3a(2) =10a(3) =33a(4) =110a(5) =369a(6) =1247a(7) =4245a(8) =14558a(9) =50295a(10) =175029a(11) =613467a(12) =2165100a(13) =7692345a(14) =27504600a(15) =98941185a(16) =357952580a(17) =1301960925a(18) =4759282415a(19) =17478557925a(20) =64468072820a(21) =238736987535a(22) =887359113700