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 A269799 #21 Apr 01 2021 09:41:51 %S A269799 0,1,1,3,22,25,717,1057,39196,98829 %N A269799 Number of vertices of the fractional perfect matching polytope for the complete graph on n vertices. %C A269799 The fractional perfect matching polytope of a graph is the set of nonnegative edge weights such that the sum of the weights of the edges incident with any given vertex equals 1. %C A269799 Sequence up to n=10 computed with PORTA (see links) by Pontus von Brömssen in December 2010. %C A269799 a(n) equals the number of facets of the polytope P_n defined in Eickmeyer and Yoshida (2008), at least up to n=10. %H A269799 Roger E. Behrend, <a href="https://doi.org/10.1016/j.laa.2013.10.001">Fractional perfect b-matching polytopes I: General theory</a>, Linear Algebra and its Applications 439 (2013), 3822-3858. %H A269799 Thomas Christof, Sebastian Schenker, <a href="http://comopt.ifi.uni-heidelberg.de/software/PORTA/">PORTA</a>, Ruprecht-Karls-Universität Heidelberg. %H A269799 K. Eickmeyer and R. Yoshida, <a href="http://arxiv.org/abs/0908.0098">The Geometry of the Neighbor-Joining Algorithm for Small Trees</a>, in: Proc. 3rd Int. Conference on Algebraic Biology, 2008, Castle of Hagenberg, Austria, Springer LNCS5147, arXiv:0908.0098 [math.CO], 2009. %e A269799 For n=4 the fractional perfect matching polytope is the convex hull of the 3 perfect matchings of K_4, so a(4)=3. For n=6, in addition to the 15 perfect matchings of K_6, the 10 pairs of disjoint triangles with edge weights 1/2 are vertices of the polytope, so a(6)=25. %Y A269799 Cf. A123023. %K A269799 nonn,more %O A269799 1,4 %A A269799 _Pontus von Brömssen_, Mar 05 2016