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A298841
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
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7
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0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 9, 6, 0, 0, 17, 21, 21, 17, 0, 0, 41, 127, 110, 127, 41, 0, 0, 104, 513, 1045, 1045, 513, 104, 0, 0, 261, 2440, 7322, 18075, 7322, 2440, 261, 0, 0, 655, 11458, 60497, 242872, 242872, 60497, 11458, 655, 0, 0, 1646, 53727, 482261, 3570731
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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...1.....3.......6........17...........41............104..............261
.0...3.....9......21.......127..........513...........2440............11458
.0...6....21.....110......1045.........7322..........60497...........482261
.0..17...127....1045.....18075.......242872........3570731.........52303834
.0..41...513....7322....242872......5918418......160441457.......4287985074
.0.104..2440...60497...3570731....160441457.....7844725524.....380985444657
.0.261.11458..482261..52303834...4287985074...380985444657...33608679844048
.0.655.53727.3886764.766622466.114829835558.18510417612668.2967985050748586
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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) +2*a(n-3)
k=3: [order 12] for n>14
k=4: [order 45] for n>48
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EXAMPLE
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Some solutions for n=5 k=5
..0..0..0..1..1. .0..0..1..1..1. .0..0..0..1..1. .0..0..0..0..0
..0..0..0..1..1. .0..0..1..1..1. .0..0..0..1..1. .0..1..1..1..0
..0..0..0..1..1. .0..0..1..1..1. .0..0..0..1..1. .0..1..1..1..0
..1..1..1..1..0. .0..1..0..0..0. .1..1..1..0..0. .0..1..1..1..0
..1..1..1..0..0. .1..1..0..0..0. .1..1..1..1..0. .0..0..0..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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