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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
0, 1, 1, 1, 1, 2, 4, 8, 18, 43, 107, 282, 771, 2167, 6241, 18421, 55309, 168845, 524728, 1649764 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)