A243772 Number of Dyck paths of semilength n having exactly three (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).

4, 5, 35, 0, 280, 1991, 4115, 34840, 96286, 309036, 1045200, 193240, 5159120, 40653929, 105545340, 603157520, 2582073261, 11015773404, 26828044860, 182118031760, 726122370210, 3026319516720, 9620891607824, 49247195403600, 161316665871200, 638742288482240

Offset

5,1

Links

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

Example

a(5) = 4: UDUDUDUUDD, UDUDUUDUDD, UDUUDUDUDD, UUDUDUDUDD.
a(6) = 5: UUDDUUDDUUDD, UUDDUUDUUDDD, UUDUUDDDUUDD, UUDUUDDUUDDD, UUDUUDUUDDDD.

Crossrefs

Column k=3 of A243752.

Main diagonal of A243829.

Sequence in context: A041907 A228662 A151450 * A332316 A243275 A269782

Adjacent sequences: A243769 A243770 A243771 * A243773 A243774 A243775

Keyword

nonn

Author

Alois P. Heinz, Jun 10 2014

Status

approved