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A198715
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T(n,k)=Number of nXk 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.
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17
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1, 1, 1, 2, 4, 2, 5, 25, 25, 5, 14, 172, 401, 172, 14, 41, 1201, 6548, 6548, 1201, 41, 122, 8404, 107042, 250031, 107042, 8404, 122, 365, 58825, 1749965, 9548295, 9548295, 1749965, 58825, 365, 1094, 411772, 28609241, 364637102, 851787199, 364637102
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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 4 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017
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LINKS
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EXAMPLE
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Table starts
....1........1............2...............5..................14
....1........4...........25.............172................1201
....2.......25..........401............6548..............107042
....5......172.........6548..........250031.............9548295
...14.....1201.......107042.........9548295...........851787199
...41.....8404......1749965.......364637102.........75987485516
..122....58825.....28609241.....13925032958.......6778819400772
..365...411772....467717288....531779578441.....604736581320925
.1094..2882401...7646461682..20307996787865...53948385378521909
.3281.20176804.125007943505.775536991678112.4812720805166620356
...
Some solutions with all values from 0 to 3 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..2..1....0..1..0..1....0..1..0..1....0..1..0..2....0..1..0..1
..1..2..0..3....2..0..3..0....2..0..1..0....1..2..1..3....1..2..3..0
..2..0..2..0....1..3..0..2....3..2..0..2....0..3..0..2....3..1..2..3
..3..2..0..1....3..2..1..0....0..3..2..1....3..1..3..0....1..3..1..0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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