%I #8 Apr 20 2013 08:17:24
%S 14,74,74,413,550,413,2268,4220,4220,2268,12574,32500,48401,32500,
%T 12574,69338,248940,541966,541966,248940,69338,383440,1910922,6127845,
%U 8952876,6127845,1910922,383440,2117054,14668206,68604790,147377704,147377704
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..2 introduced in row major order.
%C Table starts
%C ......14........74........413.........2268..........12574...........69338
%C ......74.......550.......4220........32500.........248940.........1910922
%C .....413......4220......48401.......541966........6127845........68604790
%C ....2268.....32500.....541966......8952876......147377704......2444556894
%C ...12574....248940....6127845....147377704.....3619876639.....88339585116
%C ...69338...1910922...68604790...2444556894....88339585116...3232900348158
%C ..383440..14668206..776680394..40477518336..2185708696857.118372688297292
%C .2117054.112560786.8702185466.670667507098.53385992474116
%H R. H. Hardin, <a href="/A205590/b205590.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=4 k=3
%e ..0..0..0..1....0..0..1..0....0..0..1..2....0..1..1..0....0..0..0..0
%e ..2..0..0..2....1..0..2..1....2..1..2..2....1..2..1..2....0..0..1..2
%e ..0..1..2..2....2..0..0..0....1..0..2..2....0..0..2..2....1..0..2..0
%e ..2..1..1..0....1..2..1..1....1..1..0..2....0..0..2..2....2..2..1..0
%e ..2..2..0..1....1..1..2..0....2..0..0..1....0..1..2..0....1..2..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 29 2012