A243754 Number of Dyck paths of semilength n avoiding the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

1, 0, 0, 1, 1, 9, 1, 127, 323, 1515, 4191, 10455, 20705, 93802, 113634, 3219205, 10626023, 45980364, 139604903, 555857157, 1334821448, 7577098816, 20676558270, 61994003643, 193904367362, 800928670232, 2374027931492, 12506574770693, 29311991924792

Offset: 0

Author

Alois P. Heinz, Jun 09 2014

Keywords

• nonn

Examples

			a(5) = 9 because there are 9 Dyck paths of semilength 5 avoiding the consecutive step pattern UDU given by the binary expansion of 5 = 101_2: UUDDUUDDUD, UUDDUUUDDD, UUUDDDUUDD, UUUDDUDDUD, UUUDDUUDDD, UUUUDDDDUD, UUUUDDDUDD, UUUUDDUDDD, UUUUUDDDDD.
a(6) = 1: UDUDUDUDUDUD.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..512

Crossrefs

Column k=0 of A243752.

Main diagonal of A243753.