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T(n,k)=Number of horizontal, vertical or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order
4

%I #4 Sep 13 2012 05:35:47

%S 1,1,1,2,4,2,5,25,25,5,15,279,780,279,15,52,4800,59799,59799,4800,52,

%T 203,116635,8990804,45120796,8990804,116635,203,877,3760019,

%U 2315439963,84915719366,84915719366,2315439963,3760019,877,4140,153831836

%N T(n,k)=Number of horizontal, vertical 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

%C ...1.......4.........25.........279........4800.....116635......3760019

%C ...2......25........780.......59799.....8990804.2315439963.928319229295

%C ...5.....279......59799....45120796.84915719366

%C ..15....4800....8990804.84915719366

%C ..52..116635.2315439963

%C .203.3760019

%C .877

%H R. H. Hardin, <a href="/A216663/b216663.txt">Table of n, a(n) for n = 1..39</a>

%e Some solutions for n=2 k=4

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

%e ..1..2..1..0....2..3..2..4....4..5..3..4....4..5..6..2....3..4..5..2

%Y Column 1 is A000110(n-1)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Sep 13 2012