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)(n1)(n+1))/n^2
My formula for even N is worse. It already disagrees at N=6
A(N_even)= ((2^(n^2)+ (2^(2n2))(n1)(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

