A063666 Euclidean order types: number of realizable order types of n points in the plane.

1, 2, 3, 16, 135, 3315, 158817, 14309547, 2334512907

Offset

3,2

Comments

Also the number of nonisomorphic nondegenerate acyclic rank 3 oriented matroids on n elements that are representable over the reals. - Manfred Scheucher, May 09 2022

References

O. Aichholzer, F. Aurenhammer and H. Krasser. Enumerating order types for small point sets with applications. In Proc. 17th Ann. ACM Symp. Computational Geometry, pages 11-18, Medford, Massachusetts, USA, 2001.

Links

Table of n, a(n) for n=3..11.

O. Aichholzer, F. Aurenhammer and H. Krasser, Enumerating order types for small point sets with applications

O. Aichholzer, F. Aurenhammer and H. Krasser, Enumerating order types for small point sets with applications, Order 19(3):265-281, September 2002.

Stefan Felsner and Jacob E. Goodman, Pseudoline Arrangements, Chapter 5 of Handbook of Discrete and Computational Geometry, CRC Press, 2017, see Table 5.6.1. [Specific reference for this sequence] - N. J. A. Sloane, Nov 14 2023

Stefan Felsner and J. E. Goodman, Pseudoline Arrangements. In: Toth, O'Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.

Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, Handbook of Discrete and Computational Geometry, CRC Press, 2017, see Table 5.6.1. [General reference for 2017 edition of the Handbook] - N. J. A. Sloane, Nov 14 2023

Formula

Asymptotics: a(n) = 2^(Theta(n log n)). This is Bachmann-Landau notation, that is, there are constants n_0, c, and d, such that for every n >= n_0 the inequality 2^{c n log n} <= a(n) <= 2^{d n log n} is satisfied. For more information see e.g. the Handbook of Discrete and Computational Geometry. - Manfred Scheucher, Sep 12 2019

Crossrefs

Cf. A006247.

Sequence in context: A356882 A139802 A292207 * A006247 A052318 A141309

Adjacent sequences: A063663 A063664 A063665 * A063667 A063668 A063669

Keyword

hard,more,nice,nonn

Author

Hannes Krasser (hkrasser(AT)igi.tu-graz.ac.at), Aug 22 2001

Extensions

a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002

Status

approved