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%I #4 Mar 31 2012 12:36:34
%S 2,12,12,76,252,76,492,6104,6104,492,3212,153222,636636,153222,3212,
%T 21036,3935188,72691500,72691500,3935188,21036,137932,101884208,
%U 8603604942
%N T(n,k)=Number of 2nX2k 0..2 arrays with values 0..2 introduced in row major order and each element equal to an odd number of horizontal and vertical neighbors
%C Table starts
%C .....2......12.......76......492.......3212.....21036.137932
%C ....12.....252.....6104...153222....3935188.101884208
%C ....76....6104...636636.72691500.8603604942
%C ...492..153222.72691500
%C ..3212.3935188
%C .21036
%e Some solutions for n=4 k=3
%e ..0..0..0..0..1..1....0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0
%e ..1..0..0..1..0..0....1..0..0..0..2..1....1..0..0..0..0..1....1..0..0..0..0..2
%e ..1..0..0..1..2..2....1..0..1..0..2..0....1..0..1..2..0..1....1..0..2..2..0..2
%e ..0..0..0..0..1..0....0..1..1..1..0..0....0..1..1..2..2..0....0..2..0..0..2..0
%e ..1..1..2..2..1..0....0..2..2..2..1..0....0..0..1..2..1..0....0..2..1..1..2..0
%e ..2..2..0..0..2..2....1..1..2..1..1..1....0..2..2..1..1..1....1..1..0..0..0..1
%e ..0..1..2..1..0..0....0..2..0..2..0..2....1..0..1..2..0..0....0..2..1..0..2..1
%e ..0..1..2..1..2..2....0..2..0..2..0..2....1..0..1..2..1..1....0..2..1..2..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Oct 25 2011