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%I #13 Jun 28 2017 02:10:21
%S 1,1,1,2,4,2,5,34,34,5,15,499,2027,499,15,52,10507,232841,232841,
%T 10507,52,203,272410,34003792,173549032,34003792,272410,203,876,
%U 7817980,5315840795,141168480719,141168480719,5315840795,7817980,876,4111
%N T(n,k) = number of n X k 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C Number of colorings of the grid graph P_n X P_k using a maximum of 7 colors up to permutation of the colors. - _Andrew Howroyd_, Jun 26 2017
%H Andrew Howroyd, <a href="/A198723/b198723.txt">Table of n, a(n) for n = 1..325</a> (terms 1..84 from R. H. Hardin)
%e Table starts
%e .....1............1...................2.......................5
%e .....1............4..................34.....................499
%e .....2...........34................2027..................232841
%e .....5..........499..............232841...............173549032
%e ....15........10507............34003792............141168480719
%e ....52.......272410..........5315840795.........116492275674072
%e ...203......7817980........846047363854.......96356630422085931
%e ...876....234638905.....135284283124811....79732515488691835557
%e ..4111...7176366133...21658679381667910.65980773070548173552412
%e .20648.221220625936.3468618095206638077
%e ...
%e Some solutions with all values 0 to 6 for n=3, k=3:
%e ..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..0....0..1..2
%e ..3..2..4....2..3..1....3..4..5....1..3..4....3..4..3....2..3..4....3..4..3
%e ..4..5..6....4..5..6....6..2..4....5..0..6....1..5..6....5..4..6....5..6..2
%Y Columns 1-7 are A056273(n-1), A198717, A198718, A198719, A198720, A198721, A198722.
%Y Main diagonal is A198716.
%Y Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A222340 (labeled 7 colorings), A198914 (8 colorings), A207868 (unlimited).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Oct 29 2011
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