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%I #48 Mar 12 2024 09:53:07
%S 1,2,3,16,135,3315,158817,14309547,2334512907
%N Euclidean order types: number of realizable order types of n points in the plane.
%C 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
%D 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.
%H O. Aichholzer, F. Aurenhammer and H. Krasser, <a href="http://www.ist.tugraz.at/aichholzer/research/rp/triangulations/ordertypes/">Enumerating order types for small point sets with applications</a>
%H O. Aichholzer, F. Aurenhammer and H. Krasser, <a href="https://www.researchgate.net/publication/220533854_Enumerating_Order_Types_for_Small_Point_Sets_with_Applications">Enumerating order types for small point sets with applications</a>, Order 19(3):265-281, September 2002.
%H Stefan Felsner and Jacob E. Goodman, <a href="https://www.csun.edu/~ctoth/Handbook/chap5.pdf">Pseudoline Arrangements</a>, 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
%H Stefan Felsner and J. E. Goodman, <a href="https://doi.org/10.1201/9781315119601">Pseudoline Arrangements</a>. In: Toth, O'Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.
%H Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, <a href="https://www.csun.edu/~ctoth/Handbook/HDCG3.html">Handbook of Discrete and Computational Geometry</a>, CRC Press, 2017, see Table 5.6.1. [General reference for 2017 edition of the Handbook] - _N. J. A. Sloane_, Nov 14 2023
%F 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
%Y Cf. A006247.
%K hard,more,nice,nonn
%O 3,2
%A Hannes Krasser (hkrasser(AT)igi.tu-graz.ac.at), Aug 22 2001
%E a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002
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