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Number of symmetric Euclidean pseudo-order types: nondegenerate abstract order types of configurations of n points in the plane with a nontrivial automorphism.
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%I #27 Mar 14 2021 14:06:45

%S 0,1,1,2,3,12,30,230,849,13434,76200,2392066

%N Number of symmetric Euclidean pseudo-order types: nondegenerate abstract order types of configurations of n points in the plane with a nontrivial automorphism.

%H S. 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.

%F Asymptotics: a(n) = 2^(Theta(n^2)). 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^2} <= a(n) <= 2^{d n^2} is satisfied. For more information see e.g. the Handbook of Discrete and Computational Geometry. - _Manfred Scheucher_, Sep 12 2019

%Y Cf. A006247, A325628.

%K nonn,more

%O 1,4

%A _Manfred Scheucher_ and _Günter Rote_, Sep 07 2019