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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 (list; graph; refs; listen; history; text; internal format)



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


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), 1-25.

Paolo Boldi, Sebastiano Vigna, On the lattice of antichains of finite intervals, arXiv preprint arXiv:1510.03675 [math.CO], 2015-2016.


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(n-1)/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.


Cf. A138158, A227543.

Sequence in context: A143013 A113483 A173868 * A208987 A176074 A281368

Adjacent sequences:  A274288 A274289 A274290 * A274292 A274293 A274294




N. J. A. Sloane, Jun 17 2016


a(0)=1 inserted by Sebastiano Vigna, Dec 20 2017

New name and more terms from Torsten Muetze, Nov 28 2018



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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)