# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a317541 Showing 1-1 of 1 %I A317541 #59 Sep 15 2018 15:55:20 %S A317541 0,0,0,5,18,48170,8361983 %N A317541 Number of tilings of a sphinx of order n with n^2 - 2 elementary sphinxes and a single sphinx domino that has two different tilings. %C A317541 Small areas within the sphinx that are capable of multiple tilings are important drivers of the total enumeration. %C A317541 The smallest area that can have two different tilings with the elementary sphinx is a sphinx domino. This unique domino is replaced with a single tile defect for this sequence. This domino is called a flacon. %C A317541 This replacement causes fewer tilings for sphinxes of orders six and below and more tilings for the order seven sphinx when compared to a pure sphinx tiling A279887. Figuring out why that happens makes this sequence interesting. %C A317541 The 153 order 5 pure sphinx tilings are shown in the links below. The 12 tile aspects are color coded. The blacked out areas show the tiles that change from tiling a(n) to a(n+1). Tilings #4 and #13 show the smallest areas that have two different tilings. Tilings # 63 and # 64 show that all sphinx tiles will change position in going through the 153 examples. This particular listing has tiling pairs that always share 2 or more sphinx tiles that do not change position. The sphinx tiles that change position are always edge joined. %C A317541 Combining the 12 aspects of the sphinx tile produces 46 sphinx dominoes. Sphinx domino tiling is compared with sphinx tiling in the order 4 sphinx (see link below). - _Craig Knecht_, Sep 08 2018 %H A317541 Craig Knecht, Domino sphinx tiling. %H A317541 Craig Knecht, Sequence example. %H A317541 Craig Knecht, Order 4 Sphinx. %H A317541 Craig Knecht, Order 5 sphinx 1 to 70. %H A317541 Craig Knecht, Order 5 sphinx 71 to 130. %H A317541 Craig Knecht, Order 5 sphinx 131 to 153. %H A317541 Craig Knecht, Order 6 sphinx containing 7 flacons. %H A317541 Craig Knecht, Order 7 sphinx containing 12 flacons. %H A317541 Craig Knecht, Order 7 sphinx five sphinx tile embedded shapes. %H A317541 Craig Knecht, Small symmetric sphinx tilings. %H A317541 Craig Knecht, Sphinx tile basics. %Y A317541 Cf. A279887. %K A317541 nonn,more %O A317541 0,4 %A A317541 _Craig Knecht_, Jul 30 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE