Number of Dyck paths with no UUU's and no DDD's, of semilength 2n and having exactly n (possibly overlapping) occurrences of the consecutive pattern UDUD, where U=(1,1) and D=(1,-1).

A333156

Number of Dyck paths with no UUU's and no DDD's, of semilength 2n and having exactly n (possibly overlapping) occurrences of the consecutive pattern UDUD, where U=(1,1) and D=(1,-1).

Terms

    a(0) =1a(1) =1a(2) =1a(3) =8a(4) =20a(5) =84a(6) =448a(7) =1500a(8) =8085a(9) =37895a(10) =161161a(11) =874328a(12) =4053140a(13) =19724964a(14) =103818660a(15) =499182288a(16) =2574393657a(17) =13320605595a(18) =66783194335a(19) =351243492600

External references