[seqfan] A034295(8)

Chris cgribble263 at btinternet.com
Fri Jun 7 13:12:57 CEST 2013


A034295(8) = 148.

 

All square partitions of an 8x8 square lattice are listed in
<https://oeis.org/A034295/a034295.txthttps:/oeis.org/A034295/a034295.txt>
https://oeis.org/A034295/a034295.txthttps://oeis.org/A034295/a034295.txt.

However, I do not think that the partition

   8   7   6   5   4   3   2   1

=== === === === === === === ===

   0   0   0   0   1   3   4   5

should be present.

 

If a tiling is composed of ones and zeros, where a one represents a node
with one or more links to its neighbors

and a zero represents a node with no links to its neighbors, then a tiling
for the partition

   0   0   0   0   1   3   3   9

is

 

1 1 1 1 1 1 1 1 1

1 0 0 0 1 1 0 0 1

1 0 0 0 1 1 0 0 1

1 0 0 0 1 1 1 1 1

1 1 1 1 1 0 1 0 1

1 1 1 1 1 1 1 1 1

1 0 0 1 1 1 0 0 1

1 0 0 1 0 1 0 0 1

1 1 1 1 1 1 1 1 1

 

There appears to be no way of fitting in a 4th isolated 0, representing the
central node of a 2x2 square, by moving the other squares around.

 

Please could someone verify that this is the case.

 

Thanks,

Chris Gribble

 



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