

A288568


Number of nonisomorphic connected arrangements of n pseudocircles on a sphere, in the sense that the union of the pseudocircles is a connected set, reduced for mirror symmetry.


23




OFFSET

0,4


COMMENTS

These counts have been reduced for mirror symmetry. Computed up to n=5 by Jon Wild and Christopher Jones and communicated to Neil Sloane on August 31 2016. Definition corrected Dec 10 2017 thanks to Manfred Scheucher, who has computed same result with Stefan Felsner independently.
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
See A250001, the main entry for this problem, for further information.


LINKS

Table of n, a(n) for n=0..6.
S. Felsner and M. Scheucher Homepage of Pseudocircles
S. Felsner and M. Scheucher, Arrangements of Pseudocircles: On Circularizability, arXiv:1712.02149 [cs.CG], 2017.


FORMULA

a(n) = 2^(\Theta(n^2)). (cf. Arrangements of Pseudocircles: On Circularizability)


CROSSREFS

Cf. A250001, A275923, A275924, A288554A288568, A296406, A296407A296412, A006248.
Sequence in context: A176430 A144621 A288567 * A111433 A111435 A111438
Adjacent sequences: A288565 A288566 A288567 * A288569 A288570 A288571


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Jun 13 2017, based on information supplied by Jon Wild on August 31 2016.


EXTENSIONS

a(6) from Manfred Scheucher, Dec 11 2017


STATUS

approved



