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%I #4 Aug 22 2012 19:26:20
%S 1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,5,8,8,5,2,2,15,22,78,22,15,2,5,52,
%T 364,1250,1250,364,52,5,5,203,1474,29084,24236,29084,1474,203,5,15,
%U 877,40612,908408,4851360,4851360,908408,40612,877,15,15,4140,211784,36224616
%N T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order
%C Table starts
%C ..1.....1.......1..........1...........1............2............2
%C ..1.....1.......1..........2...........5...........15...........52
%C ..1.....1.......1..........8..........22..........364.........1474
%C ..1.....2.......8.........78........1250........29084.......908408
%C ..1.....5......22.......1250.......24236......4851360....190497926
%C ..2....15.....364......29084.....4851360...1396243937.621070325112
%C ..2....52....1474.....908408...190497926.621070325112
%C ..5...203...40612...36224616.83943993818
%C ..5...877..211784.1780689974
%C .15..4140.8520924
%C .15.21147
%C .52
%H R. H. Hardin, <a href="/A215745/b215745.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=3 k=4
%e ..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
%e ..2..x..3..x....2..x..3..x....2..x..3..x....2..x..3..x....1..x..2..x
%e ..x..4..x..0....x..4..x..2....x..1..x..4....x..1..x..2....x..3..x..0
%Y Column 2 is A000110(n-2)
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_ Aug 22 2012