[seqfan] Re: A few seqs related to the Game of Life on toroidal NxN board.

[Antti Karttunen]

On Thu, Apr 15, 2010 at 1:44 PM, Antti Karttunen
<antti.karttunen at gmail.com>wrote:




> So, for case 8x8 we have about 2^64 / 8 (dihedral group) / 64 (toroidal
> rotations)
> ~ 2^55 patterns to test.


I'm probably oversimplifying and over-optimistic in that
calculation. To shed some light on this, I wonder if there
are "2D-analogues" for these sequences counting bracelets
and necklaces:
http://www.research.att.com/~njas/sequences/A000029
&
http://www.research.att.com/~njas/sequences/A000031

(that is, computed for the toroidal NxN bit-arrays)?



Cheers,

Antti Karttunen