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A316763
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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5
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0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 4, 18, 0, 0, 61, 46, 46, 61, 0, 0, 209, 151, 410, 151, 209, 0, 0, 702, 543, 2397, 2397, 543, 702, 0, 0, 2381, 2120, 13970, 26845, 13970, 2120, 2381, 0, 0, 8069, 8155, 93426, 219766, 219766, 93426, 8155, 8069, 0, 0, 27330, 30205, 586718
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OFFSET
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1,5
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COMMENTS
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Table starts
.0....0.....0.......0.........0..........0............0..............0
.0....3.....5......18........61........209..........702...........2381
.0....5.....4......46.......151........543.........2120...........8155
.0...18....46.....410......2397......13970........93426.........586718
.0...61...151....2397.....26845.....219766......2442827.......24591846
.0..209...543...13970....219766....2605126.....42857655......625815905
.0..702..2120...93426...2442827...42857655...1169271436....26888275330
.0.2381..8155..586718..24591846..625815905..26888275330...947123604065
.0.8069.30205.3677924.242436003.9056077433.613862574233.33009635701375
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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) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 18]
k=4: [order 66] for n>67
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
..1..1..0..0. .0..1..0..1. .1..0..0..1. .1..1..1..1. .1..0..0..0
..0..0..0..1. .0..0..0..0. .0..0..1..0. .1..1..0..0. .1..0..1..0
..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..0. .0..0..1..1
..1..1..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..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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