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.

830, 216, 144, 13760, 396, 144, 185348, 576, 144, 3222390, 756, 144, 57614324, 936, 144, 1033400616, 1116, 144, 18543135720, 1296, 144

Offset: 0

Author

Craig Knecht, Oct 17 2023

Keywords

• nonn
• more

Comments

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

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

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

Links

• Eurekaalert, Riddles of the sphinx, 2024.
• Greg Huber, Craig Knecht, Walter Trump, and Robert M. Ziff, Riddles of the sphinx tilings, arXiv:2304.14388 [cond-mat.stat-mech], 2023.
• Craig Knecht, Chiral color coding of the sphinx tiles in the fundamental polyads.
• Craig Knecht, Example for the sequence.
• Craig Knecht, Hemisphinx infinite polyad series.
• Craig Knecht, Infinite polyad series construction ideas.
• Craig Knecht, Infinite sphinx fundamental polyad series.
• Craig Knecht, Insert tiles in T12.
• Craig Knecht, Mapping inserts and polyads in frames with 144 tilings.
• Craig Knecht, Order 8 fundamental polyads.
• Craig Knecht, Order 12 polyad.
• Craig Knecht, Polyad overlap.

Crossrefs

Cf. A279887.

Formula

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

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

Extensions

a(12)-a(20) from Walter Trump, Oct 20 2023