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%I
%S 81,360,360,1683,1812,1683,7572,9318,9318,7572,35577,47106,57258,
%T 47106,35577,160218,243432,319698,319698,243432,160218,750426,1242930,
%U 1941084,2046168,1941084,1242930,750426,3387924,6474150,11368056,14200242
%N T(n,k) = number of (n+1) X (k+1) 0..2 arrays with no 2 X 2 subblock having the same number of clockwise edge increases as its horizontal neighbors or the same number of counterclockwise edge increases as its vertical neighbors.
%C Table starts
%C ......81......360......1683.......7572.......35577........160218.........750426
%C .....360.....1812......9318......47106......243432.......1242930........6474150
%C ....1683.....9318.....57258.....319698.....1941084......11368056.......70322310
%C ....7572....47106....319698....2046168....14200242......97476666......700650756
%C ...35577...243432...1941084...14200242...117968049.....968502540.....8557823793
%C ..160218..1242930..11368056...97476666...968502540....9838056114...108434010612
%C ..750426..6474150..70322310..700650756..8557823793..108434010612..1530071121621
%C .3387924.33323136.422623254.5009030472.75470698086.1216758803376.22248004177848
%H R. H. Hardin, <a href="/A206676/b206676.txt">Table of n, a(n) for n = 1..112</a>
%e Some solutions for n=4, k=3:
%e ..2..2..1..2....0..1..2..1....2..2..0..0....1..2..0..2....0..0..0..1
%e ..2..1..2..2....0..0..2..2....2..1..2..2....2..2..1..2....0..2..1..1
%e ..1..2..2..2....1..2..0..1....2..0..2..2....2..2..0..0....1..0..1..1
%e ..1..2..2..0....2..2..1..1....2..1..1..0....0..1..0..0....1..0..2..1
%e ..0..1..1..2....0..1..2..0....1..2..2..1....0..2..2..1....1..2..0..0
%Y Column 1 is A205513.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 11 2012
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