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A279887
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Number of tilings of a sphinx of order n by elementary sphinxes (i.e., sphinxes of order 1).
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8
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1, 1, 4, 16, 153, 71838, 5965398, 2614508085, 9822629511079, 28751930151895611, 162231215752303027270, 32813942272624544838651213, 1257159787425487037702548758466
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OFFSET
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1,3
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COMMENTS
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Sphinx tilings are, by convention, understood to be improper tilings composed of two elementary shapes, order-1 sphinxes, that are mirror images of one another. In other words, one can prove that the tiling of an order-n sphinx requires both L-sphinxes and R-sphinxes (each composed of six equilateral triangles) for any n>1. The sequence terms are based on an initial search-tree method by G. Huber, confirmed and extended by Walter Trump using backtracking and a bit-vector method.
Least-squares fitting indicates a growth law in the form of an exponential of a quadratic in n (i.e., proportional to g^(area), where g is a constant).
a(9) from analysis of the tilings and associated seam factor of two hemisphinxes of order 9 (Walter Trump, personal communication). - Greg Huber, Mar 10 2017
a(10), a(11) from double hemisphinx method described above.
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REFERENCES
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A. Martin, "The Sphinx Task Centre Problem" in C. Pritchard (ed.) The Changing Shape of Geometry, Cambridge Univ. Press, 2003, 371-378.
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LINKS
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University of Bielefeld Tilings, Sphinx.
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EXAMPLE
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For n=2, a(2)=1 and this single tiling of an order-2 L-sphinx with three elementary R-sphinxes and one elementary L-sphinx is shown in the Wikiwand link.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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