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).

1, 1, 2, 12, 69, 98, 180, 1056, 3967, 18357, 77685, 264563, 1245762, 1915056, 5303208, 24548040, 107835695, 375494210, 1898502240, 4942470942, 23489565822, 104559681798, 413327570240, 1426320927138, 6025235528016, 19911812844324, 87316285518504

Offset: 2

Author

Alois P. Heinz, Jun 10 2014

Keywords

• nonn

Examples

			a(2) = 1: (UD)[UD].
a(3) = 1: (U[U)U]DDD.
a(4) = 2: U(UDD)U[UDD], UU(UDD)[UDD].
a(5) = 12: (UD[U)DU]UDDUD, (UD[U)DU]UUDDD, (UDU)UDD[UDU]D, (UDU)[UDU]DDUD, (UDU)[UDU]UDDD, (UDU)U[UDU]DDD, UUDD(UD[U)DU]D, U(UDU)DD[UDU]D, U(UD[U)DU]DDUD, U(UD[U)DU]UDDD, U(UDU)[UDU]DDD, UU(UD[U)DU]DDD.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..350

Crossrefs

Column k=2 of A243752.

Main diagonal of A243828.