This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A190291 #17 Jul 08 2023 15:31:52
%S A190291 1,3,16,124,1262,15898,238572,4152172
%N A190291 Number of intervals in the weak (Bruhat) order of the symmetric group S_n that are distributive lattices.
%C A190291 The intervals [u,v] in the weak order that are distributive lattices are characterized by Stembridge. They are the intervals such that u^{-1}.v is fully commutative, i.e., avoids the pattern 321.
%H A190291 J. R. Stembridge, <a href="http://www.kurims.kyoto-u.ac.jp/EMIS/journals/JACO/Volume5_4/cq9j136368033131.fulltext.pdf">On the Fully Commutative Elements of Coxeter Groups</a>, Journal of Algebraic Combinatorics, 5 (1996), 353-385.
%e A190291 Example: for n=3 there are six 1-element intervals, six 2-element intervals, and four intervals that are 3-element chains, for a total of 16.
%Y A190291 Cf. A007767.
%K A190291 nonn,more
%O A190291 1,2
%A A190291 _Richard Stanley_, May 07 2011