[seqfan] Re: Towards a proof of the conjectured formula for A289233?

Joseph Myers jsm at polyomino.org.uk
Sun Dec 24 22:50:41 CET 2017

On Sun, 24 Dec 2017, jonscho at hiwaay.net wrote:

> For the cases in which n mod 12 is 3, 5, 6, or 8, such a result for  
> U-D can never hold, because it would result in noninteger values of U  
> and D.  Is there some straightforward counting argument that proves  
> that, when n mod 12 is 3, 5, 6, or 8, it's impossible to assemble all  
> the points into triples?  If so, then the exact value of A289233(n)  
> would be known for all n >= 0.

See Conway and Lagarias, Tiling with Polyominoes and Combinatorial Group 
Theory (JCTA 53 (1990), 183-208).

https://doi.org/10.1016/0097-3165(90)90057-4 (open access)

Joseph S. Myers
jsm at polyomino.org.uk

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