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%I #5 Mar 31 2012 12:36:04
%S 0,171,171,405,1773,405,3249,20097,20097,3249,12609,222003,424197,
%T 222003,12609,72225,2506851,10670517,10670517,2506851,72225,332937,
%U 28276065,254648349,560733777,254648349,28276065,332937,1731321,319126401
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock trace equal to some horizontal or vertical neighbor 2X2 subblock trace
%C Table starts
%C ........0..........171..............405...............3249...............12609
%C ......171.........1773............20097.............222003.............2506851
%C ......405........20097...........424197...........10670517...........254648349
%C .....3249.......222003.........10670517..........560733777.........29306445165
%C ....12609......2506851........254648349........29306445165.......3293066139075
%C ....72225.....28276065.......6182861913......1532963751183.....373447226493477
%C ...332937....319126401.....149296412943.....80217651167325...42234121752791535
%C ..1731321...3601102725....3610924080057...4197053176231149.4780252449901079883
%C ..8410473..40637462859...87290961055317.219601118427318765
%C .42400017.458593005339.2110537794502179
%H R. H. Hardin, <a href="/A185845/b185845.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for 4X3
%e ..1..1..2....0..0..2....1..0..0....0..0..1....2..0..1....2..2..2....0..2..0
%e ..1..2..2....1..2..2....0..0..2....1..1..2....0..0..2....2..2..2....1..2..2
%e ..1..1..1....0..1..0....1..1..2....0..0..1....0..0..2....0..1..1....0..1..2
%e ..1..1..1....1..2..1....1..0..0....2..2..2....0..0..2....0..1..0....2..2..1
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Feb 05 2011