[seqfan] nxn grids colored black and white
isaacthegreat at gmail.com
Mon Mar 26 01:33:48 CEST 2012
I had found an interesting sequence, which I computed by hand, which I am
not sure whether or not is a new sequence, or is a different statement of
an old one.
How I define it is as follows.
This sequence finds the number of nxn grids, with each cell painted black
or white, invariant under the following transformations:
Reflections (Both horizontally, vertically, and across both diagonals)
Rotations (The three of them)
And a flipping, which changes all white cells to black, and all black cells
For n=1, clearly there is only 1.
The sequence continues 4,51.
I have made wmv files of the 4 2x2 and 41 3x3 grids that can be found on my
website, and hopefully they and the previous computations are correct:
The sequence begins to share terms with A000516 <http://oeis.org/A000516>, a
similar (but to me, less natural) matrix counting sequence.
I don't quite know how to calculate additional terms, and additional terms/
input would greatly be appreciated.
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