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T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order
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%I #4 Aug 24 2012 12:56:21

%S 1,1,1,1,1,1,1,1,1,1,2,2,4,2,2,2,5,8,8,5,2,5,15,102,78,102,15,5,5,52,

%T 364,1250,1250,364,52,5,15,203,8460,29084,159712,29084,8460,203,15,15,

%U 877,40612,908408,4851360,4851360,908408,40612,877,15,52,4140,1440676

%N T(n,k)=Number of horizontal, vertical, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order

%C Table starts

%C ..1.....1.......1..........1...........2............2............5

%C ..1.....1.......1..........2...........5...........15...........52

%C ..1.....1.......4..........8.........102..........364.........8460

%C ..1.....2.......8.........78........1250........29084.......908408

%C ..2.....5.....102.......1250......159712......4851360...1590366402

%C ..2....15.....364......29084.....4851360...1396243937.621070325112

%C ..5....52....8460.....908408..1590366402.621070325112

%C ..5...203...40612...36224616.83943993818

%C .15...877.1440676.1780689974

%C .15..4140.8520924

%C .52.21147

%C .52

%H R. H. Hardin, <a href="/A215847/b215847.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for n=3 k=4

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

%e ..x..2..x..3....x..2..x..0....x..2..x..3....x..2..x..3....x..2..x..0

%e ..3..x..4..x....1..x..3..x....4..x..5..x....4..x..0..x....3..x..4..x

%Y Column 2 is A000110(n-2)

%Y Column 4 is A215741

%Y Column 6 is A215743

%K nonn,tabl

%O 1,11

%A _R. H. Hardin_ Aug 24 2012