Number of Dyck paths of semilength n having no UUUU's starting at level 0.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =13a(5) =36a(6) =105a(7) =319a(8) =1002a(9) =3235a(10) =10685a(11) =35970a(12) =123045a(13) =426667a(14) =1496782a(15) =5303623a(16) =18956417a(17) =68270576a(18) =247518777a(19) =902708185a(20) =3309559838a(21) =12190954231a(22) =45096739797a(23) =167462013888a(24) =624019924009