[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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