need guidance on Exact Cover of a Hexagon side (N) with 6 instances of n^2 connected equilateral triangles

[thomas Young]

Hello seqfans!

This may not be new:

I ask for help in verifying this claim for an OEIS sequence:  The number of ways a regular hexagon of side length n, composed of 6n² equilateral triangles, can be tiled with 6 instances of a connected figure of n² equilateral triangles is the sequence:  1, 3, 16, 216, . Mirror images are not double ocunted..

See more information and pictures at:

Link

with highest regards.

Tom Young

 

[Rémy Etc]

Thomas, I really like the construction you're proposing, and find the illustrations superb.

the solutions have rotational symmetry, only of order 3 or 6 if I'm not mistaken; it might be interesting to count the solutions for a given order.

best regards,

Rémy

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[L. Edson Jeffery]

Nice. For n large enough, if you relax the condition that all of the tiles be congruent, then more tilings are possible by combining tiles that fit together to exactly fill a rhombus with side lengths n in more than one way.

Ed Jeffery