

A018242


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


4



1, 1, 1, 1, 1, 1, 4, 11, 135, 4381, 312114, 41693377
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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.
S. Felsner and J. E. Goodman, Pseudoline Arrangements. In: Toth, O'Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.
Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359381. MR3017917. Also arXiv:1204.0645 [math.CO], 2012.  From N. J. A. Sloane, Feb 16 2013


FORMULA

Asymptotics: a(n) = 2^(Theta(n log n)). This is BachmannLandau 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.tugraz.ac.at), Feb 05 2002


STATUS

approved



