cp's OEIS Frontend

A366704 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.

%I A366704 #61 Aug 06 2025 00:52:29
%S A366704 830,216,144,13760,396,144,185348,576,144,3222390,756,144,57614324,
%T A366704 936,144,1033400616,1116,144,18543135720,1296,144
%N A366704 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 A366704 A sphinx polyad frame has at least two different sphinx tilings where each of the elementary sphinx tiles occupies a different position.
%C A366704 The frames in this sequence that have 144 sphinx tilings led to the discovery of an infinite series of sphinx polyad frames.
%C A366704 How many polyiamonds can form an infinite series of fundamental polyads?
%H A366704 Eurekaalert, <a href="https://www.eurekalert.org/news-releases/1038709">Riddles of the sphinx</a>, 2024.
%H A366704 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 A366704 Craig Knecht, <a href="/A366704/a366704.pdf">Chiral color coding of the sphinx tiles in the fundamental polyads</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704.png">Example for the sequence</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_9.png">Hemisphinx infinite polyad series</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_10.png">Infinite polyad series construction ideas</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_4.png">Infinite sphinx fundamental polyad series</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_6.png">Insert tiles in T12</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_2.png">Mapping inserts and polyads in frames with 144 tilings</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_1.png">Order 8 fundamental polyads</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_5.png">Order 12 polyad</a>.
%H A366704 Craig Knecht, <a href="/A366704/a366704_7.png">Polyad overlap</a>.
%F A366704 Conjecture: a(3*k + 2) = 144.
%F A366704 Conjecture: a(3*k + 1) = 180*k + 216.
%Y A366704 Cf. A279887.
%K A366704 nonn,more
%O A366704 0,1
%A A366704 _Craig Knecht_, Oct 17 2023
%E A366704 a(12)-a(20) from _Walter Trump_, Oct 20 2023