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 A272906 Number of topologically-distinct pizza slicings from n chords in general position. 2
 1, 1, 2, 5, 19, 130, 1814 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. 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. A054499, counting chord diagrams, is a loose lower bound. LINKS Table of n, a(n) for n=0..6. Jon Hart, 2 configurations for n=2 cuts Jon Hart, 5 configurations for n=3 cuts Jon Hart, 19 configurations for n=4 cuts Jon Hart, 130 configurations for n=5 cuts EXAMPLE 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. CROSSREFS Cf. A273280. 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. Sequence in context: A341036 A365435 A273280 * A054926 A002786 A304982 Adjacent sequences: A272903 A272904 A272905 * A272907 A272908 A272909 KEYWORD nonn,more AUTHOR Jon Hart, May 09 2016 STATUS approved

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