A366704 - OEIS

%I #55 Apr 28 2024 11:10:33

%S 830,216,144,13760,396,144,185348,576,144,3222390,756,144,57614324,

%T 936,144,1033400616,1116,144,18543135720,1296,144

%N Number of sphinx tilings of T(n+12) with a central T(n) defect where T(k) is an equilateral triangle with side length k.

%C A sphinx polyad frame has at least two different sphinx tilings where each of the elementary sphinx tiles occupies a different position.

%C The frames in this sequence that have 144 sphinx tilings led to the discovery of an infinite series of sphinx polyad frames.

%C How many polyiamonds can form an infinite series of fundamental polyads?

%H Eurekaalert, <a href="https://www.eurekalert.org/news-releases/1038709">Riddles of the sphinx</a>, 2024.

%H Greg Huber, Craig Knecht, Walter Trump, and Robert M. Ziff, <a href="https://arxiv.org/abs/2304.14388">Riddles of the sphinx tilings</a>, arXiv:2304.14388 [cond-mat.stat-mech], 2023.

%H Craig Knecht, <a href="/A366704/a366704.png">Example for the sequence</a>.

%H Craig Knecht, <a href="/A366704/a366704_9.png">Hemisphinx infinite polyad series</a>.

%H Craig Knecht, <a href="/A366704/a366704_10.png">Infinite polyad series construction ideas</a>.

%H Craig Knecht, <a href="/A366704/a366704_4.png">Infinite sphinx fundamental polyad series</a>.

%H Craig Knecht, <a href="/A366704/a366704_6.png">Insert tiles in T12</a>.

%H Craig Knecht, <a href="/A366704/a366704_2.png">Mapping inserts and polyads in frames with 144 tilings</a>.

%H Craig Knecht, <a href="/A366704/a366704_1.png">Order 8 fundamental polyads</a>.

%H Craig Knecht, <a href="/A366704/a366704_5.png">Order 12 polyad</a>.

%H Craig Knecht, <a href="/A366704/a366704_7.png">Polyad overlap</a>.

%F Conjecture: a(3*k + 2) = 144.

%F Conjecture: a(3*k + 1) = 180*k + 216.

%Y Cf. A279887.

%K nonn,more

%O 0,1

%A _Craig Knecht_, Oct 17 2023

%E a(12)-a(20) from _Walter Trump_, Oct 20 2023