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A140468 Number of points at the n-th step of the following iteration, starting with four points in general position in the real projective plane: dualize the current pointset to a family of lines, take all intersections of those lines, repeat. 9
4, 6, 7, 9, 13, 25, 97, 1741, 719725 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
K. Bezdek and J. Pach, A point set everywhere dense in the plane, Elem. Math. 40 (4) (1985) 81--84.
Joshua Cooper, Mark Walters, Iterated point-line configurations grow doubly-exponentially, Discrete Comput. Geom. 43 (2010), no. 3, 554-562. MR2587837 (2011f:51016) 51M04 (52C35).
Shalosh B. Ekhad, Doron Zeilberger, Enumerative Geometrical Genealogy (Or: The Sex Life of Points and Lines), arXiv:1406.5157 [math.CO], (19-June-2014)
D. Ismailescu and R. Radoicic, A dense planar point set from iterated line intersections Comput. Geom. 27 (2004), no. 3, 257-267.
EXAMPLE
a(2)=6 because four points in general position define six lines.
CROSSREFS
Related sequences: A244020-A244026.
Bisections A243707, A243708.
Sequence in context: A310657 A010448 A005621 * A342236 A349549 A010418
KEYWORD
hard,more,nonn
AUTHOR
Joshua Cooper (cooper(AT)math.sc.edu), Jun 28 2008
STATUS
approved

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)