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A317376
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 91, 86, 3, 5, 313, 529, 529, 313, 5, 8, 1145, 2870, 4811, 2870, 1145, 8, 13, 4184, 15382, 42512, 42512, 15382, 4184, 13, 21, 15293, 83982, 360940, 659721, 360940, 83982, 15293, 21, 34, 55895, 455180, 3113246, 9218534
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OFFSET
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1,5
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COMMENTS
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Table starts
..0.....1.......1.........2...........3.............5...............8
..1.....7......23........86.........313..........1145............4184
..1....23......91.......529........2870.........15382...........83982
..2....86.....529......4811.......42512........360940.........3113246
..3...313....2870.....42512......659721.......9218534.......134524463
..5..1145...15382....360940.....9218534.....205048072......4822465183
..8..4184...83982...3113246...134524463....4822465183....185409601420
.13.15293..455180..26916032..1959207396..113269475813...7139196864817
.21.55895.2470224.231704568.28331771091.2632551285887.270802813530242
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
k=3: [order 15] for n>16
k=4: [order 50] for n>51
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..0..0..1. .0..0..1..1
..0..1..0..1. .0..0..0..1. .1..0..0..0. .1..0..1..1. .1..1..0..1
..1..0..0..1. .0..1..1..1. .0..1..1..1. .0..1..1..1. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..1..1..1. .1..0..0..0. .0..1..0..1
..1..1..1..1. .0..1..0..0. .0..0..1..0. .0..0..0..1. .0..0..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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