[seqfan] nxn grids colored black and white

[Isaac]

Hello all,

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
to white.

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:
http://www.math.ku.edu/~ilambert/.

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.

Thanks,

Isaac L