a(n) = number of Yamanouchi words of length n that start with 3.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =5a(5) =14a(6) =44a(7) =139a(8) =475a(9) =1658a(10) =6146a(11) =23495a(12) =93840a(13) =385956a(14) =1643862a(15) =7193783a(16) =32446635a(17) =150049734a(18) =712619582a(19) =3462870079