Number of peakless Motzkin paths of length n having no (1,0)-steps at levels 0,2,4,... .

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =2a(7) =4a(8) =7a(9) =12a(10) =22a(11) =41a(12) =76a(13) =142a(14) =268a(15) =509a(16) =971a(17) =1861a(18) =3583a(19) =6925a(20) =13430a(21) =26128a(22) =50980a(23) =99735a(24) =195594a(25) =384454a(26) =757256a(27) =1494465a(28) =2954715a(29) =5851677