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A198982 T(n,k) = number of n X k 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%I A198982 #14 Jun 28 2017 02:10:37
%S A198982 1,1,1,2,4,2,5,34,34,5,15,481,1835,481,15,52,8731,146286,146286,8731,
%T A198982 52,202,174454,12662226,53082012,12662226,174454,202,855,3603244,
%U A198982 1112962873,19622872903,19622872903,1112962873,3603244,855,3845,75251971
%N A198982 T(n,k) = number of n X k 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C A198982 Number of colorings of the grid graph P_n X P_k using a maximum of 6 colors up to permutation of the colors. - _Andrew Howroyd_, Jun 26 2017
%H A198982 Andrew Howroyd, <a href="/A198982/b198982.txt">Table of n, a(n) for n = 1..325</a> (terms 1..111 from R. H. Hardin)
%e A198982 Table starts
%e A198982 .....1...........1.................2........................5
%e A198982 .....1...........4................34......................481
%e A198982 .....2..........34..............1835...................146286
%e A198982 .....5.........481............146286.................53082012
%e A198982 ....15........8731..........12662226..............19622872903
%e A198982 ....52......174454........1112962873............7267830860056
%e A198982 ...202.....3603244.......98102456246.........2692353648978984
%e A198982 ...855....75251971.....8651794282083.......997397244990907738
%e A198982 ..3845..1577395861...763087851014929....369492074075459555844
%e A198982 .18002.33105096904.67305520316532514.136880688981914387733120
%e A198982 ...
%e A198982 Some solutions with all values from 0 to 5 for n=6, k=4:
%e A198982 ..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
%e A198982 ..1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0
%e A198982 ..0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1
%e A198982 ..2..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0
%e A198982 ..1..2..0..2....4..1..0..1....3..1..0..4....3..4..2..1....3..4..2..5
%e A198982 ..4..5..2..1....5..4..2..4....5..2..3..1....1..5..1..5....5..1..5..2
%Y A198982 Columns 1-7 are A056272(n-1), A198976, A198977, A198978, A198979, A198980, A198981.
%Y A198982 Main diagonal is A198975.
%Y A198982 Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A222281 (labeled 6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).
%K A198982 nonn,tabl
%O A198982 1,4
%A A198982 _R. H. Hardin_, Nov 01 2011