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A063666
Euclidean order types: number of realizable order types of n points in the plane.
7
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
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
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