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%I #39 Nov 16 2023 08:35:26
%S 1,1,1,1,1,1,4,11,135,4381,312114,41693377
%N Number of projective order types; number of simple arrangements of n lines.
%D J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
%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 Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama, <a href="http://arxiv.org/abs/1204.0645">Complete Enumeration of Small Realizable Oriented Matroids</a>. Discrete Comput. Geom. 49 (2013), no. 2, 359-381. MR3017917. Also arXiv:1204.0645 [math.CO], 2012. - From _N. J. A. Sloane_, Feb 16 2013
%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> [<a href="https://doi.org/10.1201/9781315119601">alternative link</a>], CRC Press, 2017, see Table 5.6.1. [General reference for 2017 edition of the Handbook]
%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, A006248, A063666. A diagonal of A222317.
%K nonn,more
%O 0,7
%A _N. J. A. Sloane_
%E a(11) from Franz Aurenhammer (auren(AT)igi.tu-graz.ac.at), Feb 05 2002