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A317230
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 46, 49, 16, 32, 120, 150, 150, 120, 32, 64, 293, 488, 490, 488, 293, 64, 128, 719, 1468, 2306, 2306, 1468, 719, 128, 256, 1774, 4626, 7988, 17039, 7988, 4626, 1774, 256, 512, 4389, 14720, 29512, 101712, 101712, 29512, 14720
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....4......8.......16........32..........64..........128
...2....8....21.....49......120.......293.........719.........1774
...4...21....46....150......488......1468........4626........14720
...8...49...150....490.....2306......7988.......29512.......118116
..16..120...488...2306....17039....101712......575421......3632635
..32..293..1468...7988...101712....929233.....7953354.....80002584
..64..719..4626..29512...575421...7953354....98315821...1489532375
.128.1774.14720.118116..3632635..80002584..1489532375..35202633059
.256.4389.45811.442877.22324637.773208574.21712800613.807772568098
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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) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
k=3: [order 10] for n>12
k=4: [order 21] for n>25
k=5: [order 84] for n>88
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..1. .0..1..0..0. .0..0..1..1. .0..1..1..0
..1..1..1..1. .0..0..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
..1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..1..1
..1..1..1..1. .0..0..1..0. .0..0..1..1. .1..1..0..0. .0..0..1..1
..0..1..1..1. .1..0..0..0. .0..0..1..0. .1..0..0..0. .0..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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