A243773 Number of Dyck paths of semilength n having exactly four (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, 0, 7, 0, 14, 781, 220, 5685, 12104, 10920, 471900, 140, 402920, 10257990, 17056745, 82403580, 1152019163, 3595341849, 2413091295, 40392418220, 235442534915, 804119873760, 2973203848860, 15274217567340, 32286978092250, 94142466440960, 909684828893676

Offset

5,3

Links

Alois P. Heinz, Table of n, a(n) for n = 5..200

Example

a(5) = 1: UDUDUDUDUD.
a(7) = 7: UDUUUUUUDDDDDD, UUUUUUDDDDDDUD, UUUUUUDDDDDUDD, UUUUUUDDDDUDDD, UUUUUUDDDUDDDD, UUUUUUDDUDDDDD, UUUUUUDUDDDDDD.

Crossrefs

Column k=4 of A243752.

Main diagonal of A243830.

Sequence in context: A022920 A331423 A240825 * A097604 A240816 A007393

Adjacent sequences: A243770 A243771 A243772 * A243774 A243775 A243776

Keyword

nonn

Author

Alois P. Heinz, Jun 10 2014

Status

approved