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%I #22 Sep 26 2019 11:04:49
%S 1,1,1,3,21,984,609423
%N Number of non-isomorphic connected arrangements of n pseudo-circles on a sphere, in the sense that the union of the pseudo-circles is a connected set, reduced for mirror symmetry.
%C These counts have been reduced for mirror symmetry. Computed up to n=5 by Jon Wild and Christopher Jones and communicated to N. J. A. Sloane on August 31 2016. Definition corrected Dec 10 2017 thanks to Manfred Scheucher, who has computed same result with Stefan Felsner independently.
%C The list of arrangements is available online on the Homepage of Pseudocircles (see below) and a detailed description for the enumeration can be found in Arrangements of Pseudocircles: On Circularizability (see below). - _Manfred Scheucher_, Dec 11 2017
%C See A250001, the main entry for this problem, for further information.
%H S. Felsner and M. Scheucher <a href="http://www3.math.tu-berlin.de/pseudocircles/">Homepage of Pseudocircles</a>
%H S. Felsner and M. Scheucher, <a href="http://arxiv.org/abs/1712.02149">Arrangements of Pseudocircles: On Circularizability</a>, arXiv:1712.02149 [cs.CG], 2017.
%F a(n) = 2^(\Theta(n^2)). (cf. Arrangements of Pseudocircles: On Circularizability)
%Y Cf. A250001, A275923, A275924, A288554-A288568, A296406, A296407-A296412, A006248.
%K nonn,more
%O 0,4
%A _N. J. A. Sloane_, Jun 13 2017, based on information supplied by _Jon Wild_ on August 31 2016.
%E a(6) from _Manfred Scheucher_, Dec 11 2017
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