# [seqfan] Re: nxn grids colored black and white

Neil Sloane njasloane at gmail.com
Mon Mar 26 02:03:29 CEST 2012

```Nice sequence! I assume 41 is a typo, and you meant to say 51?

If the 51 is correct then this is probably a new sequence, and I hope you
will work out one or two more terms and submit it

This is counting orbits under the action of group, so Polya's theory
will in principle give the answer

Or maybe Ron Hardin can modify one of his programs to compute it.

The movie of the 3x3 solutions is hard to follow - for
my part I would have found a single still picture of all 51
easier to study.

Best regards

Neil

On Sun, Mar 25, 2012 at 7:33 PM, Isaac <isaacthegreat at gmail.com> wrote:

> 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
>
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Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA