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%I #5 Mar 31 2012 12:37:06
%S 81,360,360,1683,2412,1683,7572,17166,17166,7572,35577,122232,205803,
%T 122232,35577,160218,864948,2343348,2343348,864948,160218,750426,
%U 6127554,27630789,44160240,27630789,6127554,750426,3387924,43434216,312856410
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor
%C Table starts
%C ......81.......360........1683..........7572...........35577............160218
%C .....360......2412.......17166........122232..........864948...........6127554
%C ....1683.....17166......205803.......2343348........27630789.........312856410
%C ....7572....122232.....2343348......44160240.......825828828.......15535355076
%C ...35577....864948....27630789.....825828828.....25618992453......764670893556
%C ..160218...6127554...312856410...15535355076....764670893556....37886453633808
%C ..750426..43434216..3703472454..291860355624..23817299324910..1873315597879056
%C .3387924.307791390.41913844878.5480789967924.709372088422890.92643820648532838
%H R. H. Hardin, <a href="/A205520/b205520.txt">Table of n, a(n) for n = 1..144</a>
%e Some solutions for n=4 k=3
%e ..0..0..2..1....2..1..0..2....2..1..0..2....1..0..1..1....0..0..1..2
%e ..0..1..0..0....1..2..2..0....1..2..2..1....1..1..2..0....2..0..2..2
%e ..2..0..0..0....2..2..2..0....1..1..0..1....0..2..2..1....2..1..2..2
%e ..2..0..0..2....2..2..0..1....0..2..2..0....1..1..0..1....0..1..0..0
%e ..0..1..2..0....0..2..1..1....0..2..2..0....0..2..2..1....0..2..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 28 2012