

A274291


The width of the lattice of Dyck paths of length 2n ordered by the relation that one Dyck path lies above another one.


3



1, 1, 1, 2, 3, 7, 17, 44, 118, 338, 1003, 3039, 9466, 30009, 96757, 316429, 1047683, 3511473, 11876457, 40537388, 139490014, 483393651, 1686007017, 5917253784, 20879801881, 74038098051, 263793988890, 943928231920, 3390975927021, 12227214763162, 44242758258306
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OFFSET

0,4


COMMENTS

Previous name was: The width of the lattice E_n defined in the paper by Boldi and Vigna, that is, the cardinality of a maximal antichain.
a(n) is the maximum entry in row n of the triangle T(n,k) defined in A138158, or equivalently, the maximum entry in row n of the triangle T(n,k) defined in A227543. All level sizes of the lattice are given by A138158 and A227543.  Torsten Muetze, Nov 28 2018


LINKS

Torsten Muetze, Table of n, a(n) for n = 0..300
Paolo Boldi and Sebastiano Vigna, On the Lattice of Antichains of Finite Intervals, Order (2016), 125.
Paolo Boldi, Sebastiano Vigna, On the lattice of antichains of finite intervals, arXiv preprint arXiv:1510.03675 [math.CO], 20152016.


EXAMPLE

For n=4 there are 14 Dyck paths, and 1,3,3,3,2,1,1 of them have area 0,1,2,3,4,5,6, respectively, where the area is normalized to the range 0,...,n(n1)/2. These Dyck paths are UDUDUDUD (area=0), UUDDUDUD, UDUUDDUD, UDUDUUDD (area=1), UUDUDDUD, UDUUDUDD, UUDDUUDD (area=2), UUUDDDUD, UUDUDUDD, UDUUUDDD (area=3), UUUDDUDD, UUDUUDDD (area=4), UUUDUDDD (area=5), UUUUDDDD (area=6). The maximum among the numbers 1,3,3,3,2,1,1 is 3, so a(4)=3.


CROSSREFS

Cf. A138158, A227543.
Sequence in context: A143013 A113483 A173868 * A208987 A176074 A281368
Adjacent sequences: A274288 A274289 A274290 * A274292 A274293 A274294


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jun 17 2016


EXTENSIONS

a(0)=1 inserted by Sebastiano Vigna, Dec 20 2017
New name and more terms from Torsten Muetze, Nov 28 2018


STATUS

approved



