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T(n,k)=Number of horizontal, vertical, diagonal, antidiagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order
2

%I #3 Sep 15 2012 12:06:13

%S 1,1,1,2,1,2,5,4,4,5,15,34,60,34,15,52,500,2957,2957,500,52,203,10900,

%T 337731,1340534,337731,10900,203,877,322768,71786149,1842474893,

%U 1842474893,71786149,322768,877,4140,12297768,24889021634

%N T(n,k)=Number of horizontal, vertical, diagonal, antidiagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order

%C Table starts

%C ...1......1........2..........5.........15.......52.........203......877.4140

%C ...1......1........4.........34........500....10900......322768.12297768

%C ...2......4.......60.......2957.....337731.71786149.24889021634

%C ...5.....34.....2957....1340534.1842474893

%C ..15....500...337731.1842474893

%C ..52..10900.71786149

%C .203.322768

%C .877

%e Some solutions for n=3 k=4

%e ..0..2..5..6....0..3..0..2....0..3..2..3....0..3..6..3....0..3..5..0

%e ..1..3..1..3....1..4..6..4....1..4..5..6....1..4..1..2....1..4..1..2

%e ..0..4..0..4....2..5..7..8....2..3..2..3....2..5..0..7....2..3..5..6

%Y Column 1 is A000110(n-1)

%Y Column 2 is A207864(n-1)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Sep 15 2012