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%I #3 Jan 11 2013 06:30:21
%S 0,0,0,0,13,0,0,85,85,0,0,758,1828,758,0,0,5736,49197,49197,5736,0,0,
%T 44186,1160820,4072557,1160820,44186,0,0,335511,27492106,290087988,
%U 290087988,27492106,335511,0,0,2551999,645919942,20842593371
%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some king-move neighbor, with no 2-loops and with no occupancy greater than 2
%C Table starts
%C .0......0........0.........0.........0...........0.........0.......0.0
%C .0.....13.......85.......758......5736.......44186....335511.2551999
%C .0.....85.....1828.....49197...1160820....27492106.645919942
%C .0....758....49197...4072557.290087988.20842593371
%C .0...5736..1160820.290087988
%C .0..44186.27492106
%C .0.335511
%C .0
%e Some solutions for n=3 k=4
%e ..1..1..1..0....1..1..0..1....0..2..2..1....0..1..1..1....0..0..2..1
%e ..2..1..1..2....1..1..1..1....1..1..0..1....1..1..2..1....1..1..0..1
%e ..2..1..0..0....0..1..2..2....1..2..1..0....1..0..2..1....2..2..1..1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 11 2013