A063541 Least number of empty triangles determined by n points in the plane.

1, 3, 7, 13, 21, 31, 43, 58, 75, 94, 114

Offset

3,2

References

K. Dehnhardt. Leere konvexe Vielecke in ebenen Punktmengen. PhD thesis, TU Braunschweig, Germany, 1987.

Links

Table of n, a(n) for n=3..13.

O. Aichholzer and H. Krasser, The point set order type data base: a collection of applications and results, pp. 17-20 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

O. Aichholzer, R. Fabila-Monroy, T. Hackl, C. Huemer, A. Pilz, and B. Vogtenhuber. Lower bounds for the number of small convex k-holes. Computational Geometry: Theory and Applications, 47(5):605-613, 2014.

O. Aichholzer, R. Fabila-Monroy, T. Hackl, C. Huemer, A. Pilz, B. Vogtenhuber, A set of 12 points minimizing the numbers of convex 3-, 4-, and 5-holes.

O. Aichholzer, T. Hackl, and M. Scheucher, A set of 13 points minimizing the numbers of convex 3-, 4-, and 5-holes.

M. Scheucher, Counting Convex 5-Holes, Bachelor's thesis, Graz University of Technology, Austria, 2013, in German.

Crossrefs

Cf. A063542 and A276096 for empty convex 4- and 5-gons (a.k.a. k-holes), respectively. The binomial coefficient C(n,3), cf. A000292, is the number of (not necessarily empty) triangles.

Sequence in context: A002061 A247890 A353887 * A206246 A171965 A011898

Adjacent sequences: A063538 A063539 A063540 * A063542 A063543 A063544

Keyword

nonn,more

Author

N. J. A. Sloane, Aug 14 2001

Extensions

a(11)-a(13) from Manfred Scheucher, Aug 17 2018

Status

approved