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%I #8 Sep 12 2014 12:39:29
%S 2,17,17,272,2684,272,4667,511661,511661,4667,80702,101749556,
%T 1208560656,101749556,80702,1397477,20489929961,3082580273539,
%U 3082580273539,20489929961,1397477,24207692,4142124332044,8057520048724340
%N T(n,k) = Number of 2n X 2k 0..3 arrays with values 0..3 introduced in row major order and each element equal to an odd number of horizontal and vertical neighbors.
%C Table starts:
%C .......2..........17...........272..........4667............80702.......1397477
%C ......17........2684........511661.....101749556......20489929961.4142124332044
%C .....272......511661....1208560656.3082580273539.8057520048724340
%C ....4667...101749556.3082580273539
%C ...80702.20489929961
%C .1397477
%e Some solutions for n=2, k=2:
%e ..0..1..2..3....0..1..0..2....0..0..1..1....0..1..2..2....0..1..2..2
%e ..0..1..2..3....0..1..0..2....1..1..2..2....0..1..3..3....0..1..0..0
%e ..2..2..1..0....3..0..1..0....2..0..1..1....3..0..2..1....2..3..3..2
%e ..0..0..1..0....3..0..1..0....2..0..3..3....3..0..2..1....2..0..0..2
%Y Column 1 is A198287.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 27 2011