# [seqfan] Re: Occupancy count maps perfect squares

Ron Hardin rhhardin at att.net
Mon Dec 17 18:28:36 CET 2012

```Current table
T(n,k)=Number of nXk arrays of occupancy after each element moves to some
horizontal, diagonal or antidiagonal neighbor

Table starts
.0......1.........2...........4..............8.............16............32
.0......9........50.........484...........3864..........32400........267264
.0.....64......1056.......45369........1337130.......44315649....1404725868
.0....441.....21660.....4096576......438377904....56606878084.6757282699788
.0...3025....441720...367565584...142283547000.71306050492681..............
.0..20736...8997120.32940435025.46087307409528.............................
.0.142129.183206016........................................................
.0.974169..................................................................
.0.........................................................................

I'm guessing what isn't clear - maybe just explain everything differently.

1.  Put a marker at each nXk node
2.  Move each marker to a nw, ne, w, e, sw or se neighbor (but not n or s)
3.  Count the number of markers at each node. (=occupancy array)
4.  Record the number of different occupancy arrays, which is what's in the
table.

Different movement patterns can give the same occupancy array so movement count
doesn't factor occupancy count.

Eg in the case of 2x2 all-1 occupancy count, there are two movement patterns
that give it e sw e nw  and  se w ne w

rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: "franktaw at netscape.net" <franktaw at netscape.net>
> To: seqfan at list.seqfan.eu
> Sent: Mon, December 17, 2012 10:20:17 AM
> Subject: [seqfan] Re: Occupancy count maps perfect squares
>
> Please explain better. I don't see how you get anything other than
> factors  of 2, 3, 4, and 6 in these values, from the definitions given.
> Can you  perhaps give an example?
>