%I
%S 0,2,4,19,80,638,6054,76692,1137284,19405244,370597430,7825459362,
%T 180862277352
%N Number of polygonal tiles with n sides with two exits per side and n edges connecting pairs of exits, with no edges between exits on the same side and nonisomorphic under rotational and reflectional, i.e. dihedral, symmetry.
%C The case n=2 is a degenerate polygon (two sides connecting two vertices). The two possibilities are when the edges cross and do not cross. Polygons start at n=3 with a triangle.
%H Marko Riedel, <a href="https://math.stackexchange.com/questions/2097450/">Hexagonal tiles</a>
%H Marko Riedel, <a href="/A289269/a289269.maple.txt">Maple code to compute number of tiles by ordinary enumeration and by Power Group Enumeration</a>
%H Marko Riedel, <a href="/A289269/a289269_1.maple.txt">Maple code for number of tiles using Burnside lemma.</a>
%Y See A053871 for tiles with no symmetries being taken into account, A289191 for tiles with rotational symmetries only being taken into account.
%K nonn,more
%O 1,2
%A _Marko Riedel_, Jun 29 2017
