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

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =21a(6) =50a(7) =121a(8) =297a(9) =738a(10) =1854a(11) =4704a(12) =12044a(13) =31097a(14) =80919a(15) =212098a(16) =559718a(17) =1486480a(18) =3971285a(19) =10668975a(20) =28812589a(21) =78192989a(22) =213179869a(23) =583703909a(24) =1604685870a(25) =4428216295a(26) =12263271557a(27) =34074271966a(28) =94972933448a(29) =265486492798