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%I #22 Mar 13 2018 05:46:17
%S 1,1,3,3,14,12,79,56,497,311
%N Largest number of crossing-free matchings on a set S of n points in the plane, that is, a set of floor(n/2) pairwise non-intersecting segments with endpoints in S having no endpoint in common.
%H O. Aichholzer and H. Krasser, <a href="http://www.ist.tugraz.at/publications/oaich/psfiles/ak-psotd-01.ps.gz">The point set order type data base: a collection of applications and results</a>, pp. 17-20 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.
%H M. Sharir and E. Welzl. <a href="http://www.inf.ethz.ch/personal/emo/PublFiles/CrossFreeMatch_SODA17th_06.pdf">On the Number of Crossing-Free Matchings, (Cycles, and Partitions)</a>
%e The Sharir link contains an image (Figure 1) of a placement of 6 points in the plane such that 12 of their perfect matchings are crossing-free, demonstrating that a(6) >= 12. - _Nathaniel Johnston_, Nov 17 2014
%Y Cf. A063549.
%K nonn,nice,hard,more
%O 1,3
%A _N. J. A. Sloane_, Aug 14 2001
%E a(1) = a(2) = 1 inserted by _Nathaniel Johnston_, Nov 17 2014
%E Name clarified by _Manfred Scheucher_, Mar 12 2018