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A207997
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T(n,k) = number of n X k 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors).
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19
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1, 1, 1, 2, 3, 2, 4, 9, 9, 4, 8, 27, 41, 27, 8, 16, 81, 187, 187, 81, 16, 32, 243, 853, 1302, 853, 243, 32, 64, 729, 3891, 9075, 9075, 3891, 729, 64, 128, 2187, 17749, 63267, 96831, 63267, 17749, 2187, 128, 256, 6561, 80963, 441090, 1034073, 1034073, 441090, 80963
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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 3 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017
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LINKS
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FORMULA
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EXAMPLE
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Table starts
..1....1.....2.......4.........8.........16...........32............64
..1....3.....9......27........81........243..........729..........2187
..2....9....41.....187.......853.......3891........17749.........80963
..4...27...187....1302......9075......63267.......441090.......3075255
..8...81...853....9075.....96831....1034073.....11045757.....117997043
.16..243..3891...63267...1034073...16932816....277458045....4547477370
.32..729.17749..441090..11045757..277458045...6978332618..175605187731
.64.2187.80963.3075255.117997043.4547477370.175605187731.6787438272198
...
Some solutions for n=4, k=3:
..0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0
..2..0..1....2..0..2....1..0..2....1..2..1....2..0..1....1..2..1....1..2..1
..0..2..0....0..1..0....2..1..0....0..1..2....0..2..0....0..1..2....2..0..2
..1..0..1....1..2..1....1..0..1....1..2..0....2..0..2....2..0..1....1..2..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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