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
REFERENCES
Winston, Kenneth J., and Daniel J. Kleitman. "On the asymptotic number of tournament score sequences." Journal of Combinatorial Theory, Series A 35.2 (1983): 208-230. See Table 1.
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), 1-25.
Paolo Boldi, Sebastiano Vigna, On the lattice of antichains of finite intervals, arXiv preprint arXiv:1510.03675 [math.CO], 2015-2016.
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(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.
CROSSREFS
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