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.

4, 6, 7, 9, 13, 25, 97, 1741, 719725

Offset

1,1

Links

Table of n, a(n) for n=1..9.

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

Adjacent sequences: A140465 A140466 A140467 * A140469 A140470 A140471

Keyword

hard,more,nonn

Author

Joshua Cooper (cooper(AT)math.sc.edu), Jun 28 2008

Status

approved