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%I #33 Nov 20 2017 21:35:25
%S 1,1,2,5,19,130,1814
%N Number of topologically-distinct pizza slicings from n chords in general position.
%C The problem is to cut a disk with n chords, no three of which may meet at a single strictly-interior point. For each such slicing, construct the graph on vertices (pieces of the pizza) connected by edges (line segments separating two pieces). a(n) gives the number of such graphs up to isomorphism.
%C This is an empirical result, obtained from guided random trials. Independent programs agree up to and including a(5)=130. Term a(6)=1814 is unconfirmed.
%C A054499, counting chord diagrams, is a loose lower bound.
%H Jon Hart, <a href="/A272906/a272906_8.svg">2 configurations for n=2 cuts</a>
%H Jon Hart, <a href="/A272906/a272906_9.svg">5 configurations for n=3 cuts</a>
%H Jon Hart, <a href="/A272906/a272906_10.svg">19 configurations for n=4 cuts</a>
%H Jon Hart, <a href="/A272906/a272906_11.svg">130 configurations for n=5 cuts</a>
%e For n=3, there are a(3)=5 topologically distinct slicings from chords in general position. These exclude a sixth configuration found when the three chords meet at a point strictly internal to the pizza.
%Y Cf. A273280.
%Y Maximum number of regions, A000124(n), found in A090338(n) configurations. Minimum number of regions, n+1, found in A000055(n+1) configurations. Configurations can be partitioned by chord diagram, so A054499 is a (loose) lower bound.
%K nonn,more
%O 0,3
%A _Jon Hart_, May 09 2016
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