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A208054 T(n,k) = Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).

%I A208054 #11 Jun 25 2017 17:22:51
%S A208054 1,1,1,2,2,2,5,15,15,5,15,203,716,203,15,52,4140,83440,83440,4140,52,
%T A208054 203,115975,18171918,112073062,18171918,115975,203,877,4213597,
%U A208054 6423127757,346212384169,346212384169,6423127757,4213597,877,4140,190899322
%N A208054 T(n,k) = Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
%C A208054 Equivalently, the number of colorings in the rhombic hexagonal square grid graph RH_(n,k) using any number of colors up to permutation of the colors. - _Andrew Howroyd_, Jun 25 2017
%H A208054 Andrew Howroyd, <a href="/A208054/b208054.txt">Table of n, a(n) for n = 1..231</a> (terms 1..49 from R. H. Hardin)
%e A208054 Table starts
%e A208054 ...1.........1.............2................5................15
%e A208054 ...1.........2............15..............203..............4140
%e A208054 ...2........15...........716............83440..........18171918
%e A208054 ...5.......203.........83440........112073062......346212384169
%e A208054 ..15......4140......18171918.....346212384169.18633407199331522
%e A208054 ..52....115975....6423127757.2043836452962923
%e A208054 .203...4213597.3376465219485
%e A208054 .877.190899322
%e A208054 ...
%e A208054 Some solutions for n=4 k=3
%e A208054 ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
%e A208054 ..2..3..1....2..3..4....2..3..2....2..3..1....2..3..0....2..3..1....2..3..2
%e A208054 ..4..2..4....0..5..0....0..4..0....0..4..5....4..5..3....4..5..3....0..1..4
%e A208054 ..0..5..0....1..2..1....1..2..1....5..3..4....0..1..0....0..6..4....2..0..1
%Y A208054 Columns 1-5 are A000110(n-1), A020557(n-1), A208051, A208052, A208053.
%Y A208054 Cf. A207868, A212162, A212163, A208050, A068271.
%K A208054 nonn,tabl
%O A208054 1,4
%A A208054 _R. H. Hardin_, Feb 22 2012