Number of Dyck paths of semilength n having exactly two (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

A243771

Number of Dyck paths of semilength n having exactly two (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

Terms

    a(0) =1a(1) =1a(2) =2a(3) =12a(4) =69a(5) =98a(6) =180a(7) =1056a(8) =3967a(9) =18357a(10) =77685a(11) =264563a(12) =1245762a(13) =1915056a(14) =5303208a(15) =24548040a(16) =107835695a(17) =375494210a(18) =1898502240a(19) =4942470942a(20) =23489565822a(21) =104559681798a(22) =413327570240

External references