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A279887 Number of tilings of a sphinx of order n by elementary sphinxes (i.e., sphinxes of order 1). 6
1, 1, 4, 16, 153, 71838, 5965398, 2614508085, 9822629511079, 28751930151895611, 155212395372255675054 (list; graph; refs; listen; history; text; internal format)



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.


G. Huber, C. Knecht, W. Trump, and R. M. Ziff, "The Riddle of the Sphinx", 2016, unpublished.

A. Martin, "The Sphinx Task Centre Problem" in C. Pritchard (ed.) The Changing Shape of Geometry, Cambridge Univ. Press, 2003, 371-378.


Table of n, a(n) for n=1..11.

J.-Y. Lee and R. V. Moody, Lattice Substitution Systems and Model Sets, arXiv:math/0002019 [math.MG], 2000.

J.-Y. Lee and R. V. Moody, Lattice Substitution Systems and Model Sets, Discrete Comput. Geom., 25 (2001), 173-201.

Mathematics Task Centre, Task166.

University of Bielefeld Tilings, Sphinx.

Wikipedia, Sphinx tiling.

Wikiwand, Sphinx Tiling.


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.


Cf. A004003.

Sequence in context: A262123 A005749 A005739 * A226588 A318641 A005741

Adjacent sequences:  A279884 A279885 A279886 * A279888 A279889 A279890




Greg Huber, Dec 21 2016


a(9) from Greg Huber, Mar 10 2017

a(10)-a(11) from Greg Huber, May 10 2017



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Last modified June 23 23:00 EDT 2021. Contains 345402 sequences. (Running on oeis4.)