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A198906
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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.
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16
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1, 1, 1, 2, 4, 2, 5, 33, 33, 5, 15, 380, 1211, 380, 15, 51, 4801, 50384, 50384, 4801, 51, 187, 62004, 2125425, 6907736, 2125425, 62004, 187, 715, 804833, 89793204, 948656912, 948656912, 89793204, 804833, 715, 2795, 10459180, 3794115705
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..378 (terms 1..127 from R. H. Hardin)
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EXAMPLE
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Table starts
.....1..........1...............2....................5
.....1..........4..............33..................380
.....2.........33............1211................50384
.....5........380...........50384..............6907736
....15.......4801.........2125425............948656912
....51......62004........89793204.........130292546801
...187.....804833......3794115705.......17895005957823
...715...10459180....160319061892.....2457786852894234
..2795..135958401...6774239755817...337564362706067534
.11051.1767426404.286243775060868.46362726246946052884
...
Some solutions with values 0 to 4 for n=6, k=4:
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0
..0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
..2..0..2..0....2..0..3..0....2..0..2..3....2..0..1..0....2..0..1..3
..3..2..1..4....0..1..0..4....0..4..0..2....3..2..4..3....0..3..4..2
..2..4..2..1....2..4..3..1....1..3..1..4....1..0..1..2....4..0..1..4
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CROSSREFS
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Columns 1-7 are A007581(n-2), A198900, A198901, A198902, A198903, A198904, A198905.
Main diagonal is A198899.
Cf. A207997 (3 colorings), A198715 (4 colorings), A222144 (labeled 5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).
Sequence in context: A085843 A198715 A216663 * A198982 A198723 A198914
Adjacent sequences: A198903 A198904 A198905 * A198907 A198908 A198909
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Oct 31 2011
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STATUS
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approved
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