Number of Dyck paths of semilength n that do not contain the string UDDU.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =23a(6) =63a(7) =178a(8) =514a(9) =1515a(10) =4545a(11) =13827a(12) =42540a(13) =132124a(14) =413741a(15) =1304891a(16) =4141198a(17) =13214815a(18) =42375461a(19) =136478383a(20) =441285890a(21) =1431925180a(22) =4661485203a(23) =15219836738a(24) =49827678840a(25) =163535624722a(26) =537962562453