login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
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), 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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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