%I #4 Jan 12 2013 06:54:40

%S 0,0,0,0,5,0,0,39,39,0,0,292,791,292,0,0,2088,18738,18738,2088,0,0,

%T 14799,410571,1388784,410571,14799,0,0,104532,9021576,93433746,

%U 93433746,9021576,104532,0,0,737498,197291655,6308646549,18970881500,6308646549

%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2

%C Table starts

%C .0.......0..........0............0.............0.............0...............0

%C .0.......5.........39..........292..........2088.........14799..........104532

%C .0......39........791........18738........410571.......9021576.......197291655

%C .0.....292......18738......1388784......93433746....6308646549....423812250312

%C .0....2088.....410571.....93433746...18970881500.3872954657964.786996595093490

%C .0...14799....9021576...6308646549.3872954657964

%C .0..104532..197291655.423812250312

%C .0..737498.4313255090

%C .0.5200799

%C .0

%H R. H. Hardin, <a href="/A221361/b221361.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=3 k=4

%e ..0..0..2..1....1..2..0..1....1..2..1..1....0..1..1..1....1..1..2..2

%e ..2..1..0..2....2..0..1..1....2..0..0..2....2..0..2..2....1..1..1..1

%e ..0..1..2..1....2..1..0..1....1..2..0..0....2..0..0..1....0..2..0..0

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Jan 12 2013