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%I #4 Jan 25 2013 05:07:31
%S 0,0,0,0,1,0,0,3,3,0,0,8,16,8,0,0,21,92,92,21,0,0,55,536,1042,536,55,
%T 0,0,144,3125,12177,12177,3125,144,0,0,377,18216,141177,296912,141177,
%U 18216,377,0,0,987,106174,1635606,7115200,7115200,1635606,106174,987,0,0,2584
%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal or vertical neighbor, without 2-loops or left turns
%C Table starts
%C .0.....0........0..........0...........0............0.............0
%C .0.....1........3..........8..........21...........55...........144
%C .0.....3.......16.........92.........536.........3125.........18216
%C .0.....8.......92.......1042.......12177.......141177.......1635606
%C .0....21......536......12177......296912......7115200.....170234678
%C .0....55.....3125.....141177.....7115200....347487163...16949434757
%C .0...144....18216....1635606...170234678..16949434757.1685013765256
%C .0...377...106174...18947791..4073986651.827634377153
%C .0...987...618832..219496141.97465620298
%C .0..2584..3606823.2542689904
%C .0..6765.21022112
%C .0.17711
%H R. H. Hardin, <a href="/A221768/b221768.txt">Table of n, a(n) for n = 1..97</a>
%e Some solutions for n=3 k=4
%e ..0..1..0..1....1..2..1..0....0..1..1..1....1..1..1..1....1..1..1..1
%e ..1..2..0..2....1..0..1..1....1..2..1..1....2..1..1..1....1..0..0..1
%e ..1..2..1..1....1..1..2..1....1..1..1..1....1..0..1..1....1..2..2..1
%Y Column 2 is A001906(n-1)
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_ Jan 25 2013