A018242 Number of projective order types; number of simple arrangements of n lines.

1, 1, 1, 1, 1, 1, 4, 11, 135, 4381, 312114, 41693377

Offset

0,7

References

J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.

Links

Table of n, a(n) for n=0..11.

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

Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids. 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

Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth, editors, Handbook of Discrete and Computational Geometry [alternative link], CRC Press, 2017, see Table 5.6.1. [General reference for 2017 edition of the Handbook]

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, A006248, A063666. A diagonal of A222317.

Sequence in context: A214113 A167418 A055979 * A006248 A119571 A089920

Adjacent sequences: A018239 A018240 A018241 * A018243 A018244 A018245

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

Status

approved