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%I #4 Jan 06 2013 19:55:02
%S 0,1,0,2,4,0,4,8,16,0,8,81,30,64,0,16,392,2116,112,256,0,32,2500,
%T 22268,58081,418,1024,0,64,14112,488601,1319409,1612900,1560,4096,0,
%U 128,83521,7356420,103489929,78633756,44903401,5822,16384,0,256,484128,132273001
%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2
%C Table starts
%C .0.....1.....2...........4..............8.................16
%C .0.....4.....8..........81............392...............2500
%C .0....16....30........2116..........22268.............488601
%C .0....64...112.......58081........1319409..........103489929
%C .0...256...418.....1612900.......78633756........22466712321
%C .0..1024..1560....44903401.....4684821704......4919350997521
%C .0..4096..5822..1250753956...278802326676...1080371161000000
%C .0.16384.21728.34842328921.16577412686597.237502965724417600
%C Even columns are perfect squares
%H R. H. Hardin, <a href="/A221255/b221255.txt">Table of n, a(n) for n = 1..126</a>
%e Some solutions for n=3 k=4
%e ..1..2..1..0....0..2..2..0....0..2..2..1....0..2..2..1....1..1..0..1
%e ..0..2..1..2....0..2..1..0....0..1..1..1....1..0..1..1....1..1..1..1
%e ..2..0..1..0....2..1..1..1....2..1..1..0....1..1..1..1....1..1..2..1
%Y Column 2 is A000302(n-1)
%Y Column 3 is A052530
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_ Jan 06 2013