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A232941
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T(n,k)=Number of nXk 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, vertically or antidiagonally
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8
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3, 6, 6, 12, 12, 12, 24, 26, 26, 24, 48, 56, 84, 56, 48, 96, 120, 252, 252, 120, 96, 192, 258, 774, 1048, 774, 258, 192, 384, 554, 2360, 4458, 4458, 2360, 554, 384, 768, 1190, 7212, 18850, 26644, 18850, 7212, 1190, 768, 1536, 2556, 22024, 79810, 157322, 157322
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OFFSET
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1,1
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COMMENTS
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Table starts
....3....6.....12......24........48.........96..........192...........384
....6...12.....26......56.......120........258..........554..........1190
...12...26.....84.....252.......774.......2360.........7212.........22024
...24...56....252....1048......4458......18850........79810........337850
...48..120....774....4458.....26644.....157322.......932576.......5521380
...96..258...2360...18850....157322....1294504.....10700160......88318190
..192..554...7212...79810....932576...10700160....123516664....1422959686
..384.1190..22024..337850...5521380...88318190...1422959686...22870954236
..768.2556..67272.1430144..32701386..729295244..16403819514..367894792064
.1536.5490.205466.6054098.193661452.6021446660.189062126148.5916284262276
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
k=3: a(n) = a(n-1) +5*a(n-2) +4*a(n-3) -a(n-5) for n>6
k=4: [order 8] for n>9
k=5: [order 13] for n>14
k=6: [order 21] for n>22
k=7: [order 34] for n>35
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EXAMPLE
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Some solutions for n=5 k=4
..1..2..2..1....2..2..2..2....2..2..2..2....1..0..1..0....2..2..2..2
..2..2..2..2....2..2..2..1....2..2..1..2....0..0..0..1....2..2..2..2
..2..2..2..2....1..2..2..2....2..2..2..2....0..0..0..0....2..2..2..1
..2..1..2..1....2..2..2..2....1..2..2..2....1..0..0..1....2..2..2..2
..2..2..2..2....2..1..2..1....2..1..2..2....0..1..0..0....2..1..2..2
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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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