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A289191 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 symmetry. 4
0, 2, 4, 22, 112, 1060, 11292, 149448, 2257288, 38720728, 740754220, 15648468804, 361711410384 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..13.

Marko Riedel, Hexagonal tiles.

Marko Riedel, Maple code to compute number of tiles by ordinary enumeration and by Power Group Enumeration.

Marko Riedel, Maple code for number of tiles using Burnside lemma.


See A053871 for tiles with no rotational symmetries being taken into account, A289269 for tiles with rotational and reflectional symmetries being taken into account, A289343 for the same statistic evaluated when n is prime.

Sequence in context: A047035 A080042 A165588 * A235938 A279705 A321248

Adjacent sequences:  A289188 A289189 A289190 * A289192 A289193 A289194




Marko Riedel, Jun 27 2017



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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)