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A198906 T(n,k) = number of n X k 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%I A198906 #14 Jun 28 2017 02:10:26
%S A198906 1,1,1,2,4,2,5,33,33,5,15,380,1211,380,15,51,4801,50384,50384,4801,51,
%T A198906 187,62004,2125425,6907736,2125425,62004,187,715,804833,89793204,
%U A198906 948656912,948656912,89793204,804833,715,2795,10459180,3794115705
%N A198906 T(n,k) = number of n X k 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C A198906 Number of colorings of the grid graph P_n X P_k using a maximum of 5 colors up to permutation of the colors. - _Andrew Howroyd_, Jun 26 2017
%H A198906 Andrew Howroyd, <a href="/A198906/b198906.txt">Table of n, a(n) for n = 1..378</a> (terms 1..127 from R. H. Hardin)
%e A198906 Table starts
%e A198906 .....1..........1...............2....................5
%e A198906 .....1..........4..............33..................380
%e A198906 .....2.........33............1211................50384
%e A198906 .....5........380...........50384..............6907736
%e A198906 ....15.......4801.........2125425............948656912
%e A198906 ....51......62004........89793204.........130292546801
%e A198906 ...187.....804833......3794115705.......17895005957823
%e A198906 ...715...10459180....160319061892.....2457786852894234
%e A198906 ..2795..135958401...6774239755817...337564362706067534
%e A198906 .11051.1767426404.286243775060868.46362726246946052884
%e A198906 ...
%e A198906 Some solutions with values 0 to 4 for n=6, k=4:
%e A198906 ..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
%e A198906 ..1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0
%e A198906 ..0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
%e A198906 ..2..0..2..0....2..0..3..0....2..0..2..3....2..0..1..0....2..0..1..3
%e A198906 ..3..2..1..4....0..1..0..4....0..4..0..2....3..2..4..3....0..3..4..2
%e A198906 ..2..4..2..1....2..4..3..1....1..3..1..4....1..0..1..2....4..0..1..4
%Y A198906 Columns 1-7 are A007581(n-2), A198900, A198901, A198902, A198903, A198904, A198905.
%Y A198906 Main diagonal is A198899.
%Y A198906 Cf. A207997 (3 colorings), A198715 (4 colorings), A222144 (labeled 5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).
%K A198906 nonn,tabl
%O A198906 1,4
%A A198906 _R. H. Hardin_, Oct 31 2011