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Re: Tiling the plane with checkerboard patterns
Posted:
Jul 15, 2010 7:31 AM


> 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 foolproof > 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:
n=7 Mat_7=[1 1 24 x x ...] Sum_7=[1 1 24 .......]
n=8 Mat_8=[1 1 33 x x ...] Sum_8=[1 1 63 .......]
n=9 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, Avni



