Number of peakless Motzkin paths of length n having no (1,0)-steps at levels 1,3,5,... .

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =4a(7) =7a(8) =12a(9) =21a(10) =38a(11) =70a(12) =130a(13) =243a(14) =457a(15) =865a(16) =1647a(17) =3152a(18) =6059a(19) =11693a(20) =22647a(21) =44007a(22) =85770a(23) =167626a(24) =328430a(25) =644993a(26) =1269413a(27) =2503339a(28) =4945897a(29) =9788700