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A275565
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T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.
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12
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1, 2, 2, 3, 14, 3, 6, 36, 54, 6, 12, 96, 126, 216, 12, 24, 288, 294, 504, 864, 24, 48, 864, 672, 1176, 1872, 3456, 48, 96, 2592, 1536, 3192, 4056, 7200, 13824, 96, 192, 7776, 3552, 8664, 13104, 15000, 27360, 55296, 192, 384, 23328, 8214, 23712, 42336, 57600
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OFFSET
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1,2
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COMMENTS
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Table starts
...1......2.......3.......6.......12........24.........48..........96
...2.....14......36......96......288.......864.......2592........7776
...3.....54.....126.....294......672......1536.......3552........8214
...6....216.....504....1176.....3192......8664......23712.......64896
..12....864....1872....4056....13104.....42336.....138600......453750
..24...3456....7200...15000....57600....221184.....867456.....3402054
..48..13824...27360...54150...248520...1140576....5360184....25190406
..96..55296..104256..196566..1075140...5880600...33275880...188294424
.192.221184..397440..714150..4663710..30456054..206892990..1405458150
.384.884736.1513728.2589894.20186982.157347846.1286374716.10516571736
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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) for n>3
k=2: a(n) = 4*a(n-1) for n>3
k=3: a(n) = 2*a(n-1) +8*a(n-2) -16*a(n-4) for n>5
k=4: [order 10] for n>11
k=5: [order 32] for n>34
k=6: [order 35] for n>37
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>3
n=2: a(n) = 3*a(n-1) for n>4
n=3: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +7*a(n-5) -5*a(n-6) +2*a(n-8) -a(n-9) for n>10
n=4: [order 25] for n>28
n=5: [order 63] for n>66
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..2..2. .0..1..1..2. .0..1..2..2. .0..1..2..0. .0..1..2..0
..1..0..0..1. .0..1..2..0. .1..0..0..2. .0..1..1..2. .1..1..2..2
..2..2..1..1. .1..2..2..1. .1..0..0..1. .2..0..1..1. .1..0..0..2
..2..2..1..0. .1..0..0..1. .2..2..1..1. .2..2..0..1. .2..0..0..1
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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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