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A063666 Euclidean order types: number of realizable order types of n points in the plane. 6
1, 2, 3, 16, 135, 3315, 158817, 14309547, 2334512907 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

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

Table of n, a(n) for n=3..11.

O. Aichholzer, F. Aurenhammer and H. Krasser, Enumerating order types for small point sets with applications

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.

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 fulfilled. For more information see e.g. the Handbook of Discrete and Computational Geometry. - Manfred Scheucher, Sep 12 2019

CROSSREFS

Cf. A006247.

Sequence in context: A269067 A139802 A292207 * A006247 A052318 A141309

Adjacent sequences:  A063663 A063664 A063665 * A063667 A063668 A063669

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

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Last modified July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)