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

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =21a(6) =51a(7) =126a(8) =316a(9) =799a(10) =2034a(11) =5202a(12) =13357a(13) =34407a(14) =88888a(15) =230237a(16) =597829a(17) =1555962a(18) =4058944a(19) =10612102a(20) =27807135a(21) =73025751a(22) =192204957a(23) =507025163a(24) =1340545113a(25) =3552492126