%I #13 Jun 28 2017 02:10:32

%S 1,1,1,2,4,2,5,34,34,5,15,500,2051,500,15,52,10867,269940,269940,

%T 10867,52,203,313132,54381563,319608038,54381563,313132,203,877,

%U 10856948,13088156547,481871809749,481871809749,13088156547,10856948,877,4139

%N T(n,k) = number of n X k 0..7 arrays with values 0..7 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 8 colors up to permutation of the colors. - _Andrew Howroyd_, Jun 26 2017

%H Andrew Howroyd, <a href="/A198914/b198914.txt">Table of n, a(n) for n = 1..276</a> (terms 1..71 from R. H. Hardin)

%e Table starts

%e .....1............1..................2......................5

%e .....1............4.................34....................500

%e .....2...........34...............2051.................269940

%e .....5..........500.............269940..............319608038

%e ....15........10867...........54381563...........481871809749

%e ....52.......313132........13088156547........769126451071174

%e ...203.....10856948......3352514013159....1243368053336112649

%e ...877....418689772....876632051686733.2015791720035206825303

%e ..4139..17067989413.230783525290600476

%e .21110.715189507700

%e ...

%e Some solutions with values 0 to 7 for n=5, k=3:

%e ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0

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

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

%e ..2..4..5....5..4..3....5..6..1....5..3..6....6..7..0....5..6..7....1..5..1

%e ..1..6..7....6..0..7....6..7..2....7..4..2....3..0..3....7..0..5....6..7..4

%Y Columns 1-7 are A099262(n-1), A198908, A198909, A198910, A198911, A198912, A198913.

%Y Main diagonal is A198907.

%Y Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A222462 (labeled 8 colorings), A207868 (unlimited).

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Oct 31 2011