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A316289
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 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, 42, 49, 16, 32, 120, 125, 125, 120, 32, 64, 293, 361, 354, 361, 293, 64, 128, 719, 987, 1372, 1372, 987, 719, 128, 256, 1774, 2840, 3933, 7973, 3933, 2840, 1774, 256, 512, 4389, 8177, 12454, 35706, 35706, 12454, 8177, 4389
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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....8....21.....49.....120......293.......719........1774.........4389
...4...21....42....125.....361......987......2840........8177........23078
...8...49...125....354....1372.....3933.....12454.......42946.......135396
..16..120...361...1372....7973....35706....164734......838632......4054621
..32..293...987...3933...35706...205946...1262767.....8828402.....57330292
..64..719..2840..12454..164734..1262767..10464990...101136854....901515338
.128.1774..8177..42946..838632..8828402.101136854..1363011634..17053088411
.256.4389.23078.135396.4054621.57330292.901515338.17053088411.297013482603
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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 85] for n>89
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0
..0..0..0..1. .0..0..1..1. .1..1..1..1. .0..1..1..0. .0..1..0..0
..0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..1..0. .0..0..0..0
..0..1..1..1. .1..0..0..0. .1..0..1..1. .0..0..0..0. .0..0..1..0
..1..1..1..0. .1..1..0..1. .1..1..1..1. .1..0..0..0. .0..1..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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