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

%I #4 Sep 14 2012 06:22:35

%S 1,1,1,2,2,2,5,9,9,5,15,90,189,90,15,52,1451,11730,11730,1451,52,203,

%T 33694,1561834,6901440,1561834,33694,203,877,1047754,370625430,

%U 11239872497,11239872497,370625430,1047754,877,4140,41569451

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

%C ...1.......2.........9..........90........1451.....33694......1047754.41569451

%C ...2.......9.......189.......11730.....1561834.370625430.139733635588

%C ...5......90.....11730.....6901440.11239872497

%C ..15....1451...1561834.11239872497

%C ..52...33694.370625430

%C .203.1047754

%C .877

%H R. H. Hardin, <a href="/A216694/b216694.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..2..3....0..1..2..3....0..1..2..1....0..1..2..1

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

%Y Column 1 is A000110(n-1)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Sep 14 2012