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A230819
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T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero
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7
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0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 12, 12, 2, 0, 0, 12, 100, 174, 100, 12, 0, 0, 18, 326, 816, 816, 326, 18, 0, 0, 56, 2114, 12210, 28772, 12210, 2114, 56, 0, 0, 170, 9226, 108006, 497166, 497166, 108006, 9226, 170, 0, 0, 420, 47220, 1202184, 10872238
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OFFSET
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1,8
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COMMENTS
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Table starts
.0..0....0.......0.........0...........0.............0.............0
.0..0....2.......0.........2..........12............18............56
.0..2....4......12.......100.........326..........2114..........9226
.0..0...12.....174.......816.......12210........108006.......1202184
.0..2..100.....816.....28772......497166......10872238.....222626294
.0.12..326...12210....497166....21835516.....888633610...37511690680
.0.18.2114..108006..10872238...888633610...75341251814.6484756891722
.0.56.9226.1202184.222626294.37511690680.6484756891722
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LINKS
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FORMULA
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Empirical for column k:
k=2: a(n) = 2*a(n-1) +a(n-2) +4*a(n-3) -4*a(n-4)
k=3: [order 19]
k=4: [order 95] for n>96
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EXAMPLE
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Some solutions for n=4 k=4
..0..2..1..0....0..2..1..0....0..1..2..1....0..1..0..2....0..1..2..0
..1..0..0..2....1..0..1..2....2..1..0..0....2..2..0..1....2..0..2..1
..2..0..1..1....2..0..0..0....0..1..2..2....1..0..1..2....1..2..0..2
..0..1..2..0....0..1..2..1....2..1..0..1....0..2..1..0....0..2..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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