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Topic: Tiling the plane with checkerboard patterns
Replies: 21   Last Post: Jul 14, 2010 10:33 PM

 Messages: [ Previous | Next ]
 mark Posts: 206 Registered: 12/6/04
Re: Tiling the plane with checkerboard patterns
Posted: Jul 11, 2010 12:00 AM

I just checked my formula against Avni's extended list. We are very close. My odd N formula agrees at N=7 and disagrees slightly at N=9.

A(N_odd)= ((2^(n^2)+ (2^n)(n-1)(n+1))/n^2

My formula for even N is worse. It already disagrees at N=6

A(N_even)= ((2^(n^2)+ (2^(2n-2))(n-1)(n+1))/n^2

Note: If this chart does not display properly, viewing as text might help.

> n a(n,Avni) a(n,Mark)
> 1 2 2
> 2 7 7
> 3 64 64
> 4 4156 4156
> 5 1342208 1342208
> 6 1908874521 1908875349 1/3
> 7 11488774559744 11488774559744
> 8 288230376151712689 288230376151727872
> 9 29850020237398251228192 29850020237398251227818 2/3

Date Subject Author
7/6/10 Rouben Rostamian
7/7/10 Avni Pllana
7/8/10 mark
7/9/10 Rouben Rostamian
7/9/10 Avni Pllana
7/9/10 Rouben Rostamian
7/10/10 Avni Pllana
7/10/10 mark
7/11/10 Rouben Rostamian
7/11/10 mark
7/11/10 Rouben Rostamian
7/11/10 mark
7/12/10 Rouben Rostamian
7/13/10 mark
7/14/10 Rouben Rostamian
7/14/10 mark
7/11/10 Rouben Rostamian
7/14/10 Avni Pllana
7/14/10 Rouben Rostamian
7/13/10 Mary Krimmel
7/14/10 Rouben Rostamian
7/14/10 mark