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Topic: Tiling the plane with checkerboard patterns
Replies: 2   Last Post: Jul 16, 2010 8:39 AM

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Avni Pllana

Posts: 546
Registered: 12/6/04
Re: Tiling the plane with checkerboard patterns
Posted: Jul 15, 2010 7:31 AM
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> Hello Avni, I am surprised with the discrepancy you
> have found
> in the a(6) case. I still hold hope that your
> formula does
> give the correct values for all a(n). Could it be
> that the
> discrepancy is due to Matlab's floating point
> arithmetic?
> Since you and Mark have both noted the effect of
> parity of n,
> I want to point out that I have reason to believe
> that what
> matters is not whether n is odd or even, but whether
> it is
> prime or composite. I don't have a fool-proof
> argument to
> support that right now; just a preliminary analysis.
> I will write about this again if I find out more.
> Rouben

Hi Rouben,

some results for n=7,8,9 are shown below:

Mat_7=[1 1 24 x x ...]
Sum_7=[1 1 24 .......]

Mat_8=[1 1 33 x x ...]
Sum_8=[1 1 63 .......]

Mat_9=[1 1 40 x x ...]
Sum_9=[1 1 40 .......]

The above results suggest that discrepancy has to with the parity of n and not with the primeness of n.

Best regards,

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