A193617 Maximum cardinality of a subset of Dyck n-paths p that share both the same area and the same maj(beta(p)) statistic.

0, 1, 1, 1, 1, 2, 4, 8, 18, 43, 107, 282, 771, 2167, 6241, 18421, 55309, 168845, 524728, 1649764

Offset

0,6

Comments

The maj(beta(p)) statistic is the major index of the "billiard ball" path under p.

Links

Table of n, a(n) for n=0..19.

Jason Bandlow and Kendra Killpatrick, An Area-to-Inv Bijection Between Dyck Paths and 312-avoiding Permutations

Example

For n=8 there are 18 paths with area = 9 and maj(beta(p)) = 10 (and vice versa). No other conforming subset of Dyck 8-paths has greater cardinality.

Crossrefs

Sequence in context: A318850 A052327 A059221 * A233139 A308246 A114203

Adjacent sequences: A193614 A193615 A193616 * A193618 A193619 A193620

Keyword

nonn

Author

David Scambler, Jul 31 2011

Status

approved