%I #4 Mar 31 2012 12:36:34

%S 2,17,17,272,2452,272,4667,413375,413375,4667,80702,72559212,

%T 706120206,72559212,80702,1397477,12940532183,1275102148950,

%U 1275102148950,12940532183,1397477,24207692,2322145946560,2366880827870877

%N T(n,k)=Number of 2nX2k 0..3 arrays with values 0..3 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor

%C Table starts

%C .......2..........17...........272..........4667............80702.......1397477

%C ......17........2452........413375......72559212......12940532183.2322145946560

%C .....272......413375.....706120206.1275102148950.2366880827870877

%C ....4667....72559212.1275102148950

%C ...80702.12940532183

%C .1397477

%e Some solutions for n=4 k=2

%e ..0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..0

%e ..0..1..2..1....0..1..2..1....0..1..2..1....0..1..2..1....0..1..2..1

%e ..2..3..2..1....1..0..2..1....2..0..2..1....2..3..2..1....2..0..2..1

%e ..2..3..0..0....1..0..3..3....2..0..3..3....2..3..0..0....2..0..3..3

%e ..0..2..1..3....3..3..1..2....0..3..0..2....1..1..2..3....3..1..0..1

%e ..0..2..1..3....0..0..1..2....0..3..0..2....3..3..2..3....3..1..0..1

%e ..1..3..3..0....1..3..0..1....3..2..1..1....2..1..1..2....0..0..2..0

%e ..1..2..2..0....1..3..0..1....3..2..0..0....2..0..0..2....3..3..2..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Oct 23 2011