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A316218
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 28, 28, 16, 32, 94, 75, 75, 94, 32, 64, 284, 250, 310, 250, 284, 64, 128, 752, 706, 1468, 1468, 706, 752, 128, 256, 2244, 2116, 5883, 8943, 5883, 2116, 2244, 256, 512, 6532, 6399, 25093, 44018, 44018, 25093, 6399, 6532, 512
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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..........256
...2....4....14.....28......94......284........752........2244.........6532
...4...14....28.....75.....250......706.......2116........6399........19179
...8...28....75....310....1468.....5883......25093......108869.......463940
..16...94...250...1468....8943....44018.....242149.....1355516......7364630
..32..284...706...5883...44018...273102....1906841....13506787.....92623868
..64..752..2116..25093..242149..1906841...17524746...162191532...1448194529
.128.2244..6399.108869.1355516.13506787..162191532..1966735514..22731828021
.256.6532.19179.463940.7364630.92623868.1448194529.22731828021.338897042438
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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) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
k=3: [order 15] for n>16
k=4: [order 62] for n>64
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..1
..1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
..1..1..1..1. .1..1..1..0. .0..1..1..0. .1..0..0..0. .1..0..0..0
..0..0..1..1. .1..1..1..1. .0..1..1..0. .0..0..0..0. .0..0..1..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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