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A289269 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 non-isomorphic under rotational and reflectional, i.e. dihedral, symmetry. 3

%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 non-isomorphic 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

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Last modified November 20 15:02 EST 2018. Contains 317402 sequences. (Running on oeis4.)