Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Jan 09 2013 08:34:52
%S 0,0,0,0,4,0,1,4,0,0,0,25,0,16,0,0,52,100,16,0,0,0,196,0,1089,0,64,0,
%T 1,520,0,4920,6724,64,0,0,0,1681,0,94864,0,56644,0,256,0,0,4840,46656,
%U 707600,0,626424,400689,256,0,0,0,14884,0,9517225,0,62220544,0,3122289,0
%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with every occupancy equal to zero or two
%C Table starts
%C .0....0...0.......1......0........0......0.........1........0.....0.....0.1
%C .0....4...4......25.....52......196....520......1681.....4840.14884.44044
%C .0....0...0.....100......0........0......0.....46656........0.....0
%C .0...16..16....1089...4920....94864.707600...9517225.87086136
%C .0....0...0....6724......0........0......0.644652100
%C .0...64..64...56644.626424.62220544
%C .0....0...0..400689......0
%C .0..256.256.3122289
%C .0....0...0
%C .0.1024
%C .0
%C Even columns are perfect squares
%H R. H. Hardin, <a href="/A221275/b221275.txt">Table of n, a(n) for n = 1..71</a>
%e Some solutions for n=4 k=4
%e ..0..0..0..2....0..0..0..0....0..0..0..2....2..2..2..0....0..0..2..0
%e ..2..2..2..0....2..2..2..2....2..2..2..0....0..2..0..2....2..2..2..2
%e ..2..2..0..0....0..0..0..2....0..2..2..2....2..2..2..0....0..0..0..2
%e ..0..2..2..0....2..2..2..0....2..0..0..0....0..0..0..0....0..2..2..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 09 2013