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A232955
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T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero
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13
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1, 3, 4, 9, 21, 16, 27, 129, 147, 64, 81, 771, 1881, 1029, 256, 243, 4629, 22971, 27441, 7203, 1024, 729, 27771, 283131, 685251, 400329, 50421, 4096, 2187, 166629, 3484893, 17429409, 20442651, 5840289, 352947, 16384, 6561, 999771, 42904365, 442227825
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OFFSET
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1,2
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COMMENTS
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Table starts
......1.........3............9..............27.................81
......4........21..........129.............771...............4629
.....16.......147.........1881...........22971.............283131
.....64......1029........27441..........685251...........17429409
....256......7203.......400329........20442651.........1074244299
...1024.....50421......5840289.......609853251........66226131273
...4096....352947.....85202361.....18193384251......4082986991091
..16384...2470629...1242993681....542752261251....251727862281441
..65536..17294403..18133691049..16191600916251..15519780149309307
.262144.121060821.264547403649.483034266181251.956841601733733945
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1)
k=2: a(n) = 7*a(n-1)
k=3: a(n) = 15*a(n-1) -6*a(n-2)
k=4: a(n) = 31*a(n-1) -35*a(n-2) +5*a(n-3)
k=5: [order 10]
k=6: [order 21]
Empirical for row n:
n=1: a(n) = 3*a(n-1)
n=2: a(n) = 5*a(n-1) +6*a(n-2)
n=3: a(n) = 12*a(n-1) +7*a(n-2) -40*a(n-3) +12*a(n-4)
n=4: [order 10]
n=5: [order 26] for n>27
n=6: [order 86] for n>87
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EXAMPLE
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Some solutions for n=3 k=4
..0..2..3..2....0..1..3..3....0..1..0..2....0..1..0..0....0..2..0..2
..2..2..3..3....0..1..1..1....3..2..0..1....0..2..0..0....2..0..2..2
..0..2..3..3....0..1..0..0....2..2..3..2....0..2..0..2....1..0..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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