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A298139
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
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6
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0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 0, 10, 0, 13, 0, 0, 34, 3, 20, 20, 3, 34, 0, 0, 65, 6, 68, 88, 68, 6, 65, 0, 0, 123, 23, 185, 242, 242, 185, 23, 123, 0, 0, 266, 68, 561, 627, 917, 627, 561, 68, 266, 0, 0, 499, 205, 1600, 2604, 3417, 3417, 2604
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OFFSET
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1,8
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COMMENTS
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Table starts
.0...0..0....0....0.....0......0.......0........0.........0.........0
.0...1..3....2...11....13.....34......65......123.......266.......499
.0...3..0....3....0.....3......6......23.......68.......205.......572
.0...2..3...10...20....68....185.....561.....1600......4856.....14490
.0..11..0...20...88...242....627....2604.....8137.....28727....101137
.0..13..3...68..242...917...3417...14533....58845....244155...1024766
.0..34..6..185..627..3417..14422...73961...354200...1772595...8807624
.0..65.23..561.2604.14533..73961..467043..2633905..15796516..93682029
.0.123.68.1600.8137.58845.354200.2633905.17828062.127068717.899366629
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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)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
k=3: [order 17] for n>18
k=4: [order 60] for n>61
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..1..0..1. .1..0..1..1. .0..1..0..1. .0..1..0..1. .1..0..1..0
..1..0..1..0. .0..1..0..1. .1..0..1..0. .1..0..0..1. .1..0..1..0
..1..0..0..0. .0..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..1..0
..0..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..1..0. .1..0..1..0
..0..0..1..1. .1..1..0..0. .1..1..1..1. .0..0..0..0. .1..1..0..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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