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A305482
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 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, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 31, 21, 21, 31, 13, 21, 49, 40, 48, 40, 49, 21, 34, 103, 70, 98, 98, 70, 103, 34, 55, 193, 125, 192, 277, 192, 125, 193, 55, 89, 327, 231, 368, 577, 577, 368, 231, 327, 89, 144, 641, 419, 732, 1245, 1558, 1245, 732, 419, 641
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OFFSET
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1,2
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COMMENTS
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Table starts
..1...2...3....5....8....13.....21.....34......55......89......144.......233
..2...5...7...17...31....49....103....193.....327.....641.....1207......2129
..3...7..10...21...40....70....125....231.....419.....752.....1365......2482
..5..17..21...48...98...192....368....732....1480....2932.....5776.....11486
..8..31..40...98..277...577...1245...2868....6381...14206....31630.....70391
.13..49..70..192..577..1558...3910..10465...27679...70960...185085....482009
.21.103.125..368.1245..3910..11438..34687..106558..317866...952180...2866802
.34.193.231..732.2868.10465..34687.123104..440388.1501195..5216253..18221847
.55.327.419.1480.6381.27679.106558.440388.1894686.7620015.31132355.129187191
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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) = a(n-1) +4*a(n-3) -2*a(n-4) for n>5
k=3: a(n) = a(n-1) +3*a(n-3) -2*a(n-6) for n>9
k=4: [order 10] for n>13
k=5: [order 29] for n>33
k=6: [order 60] for n>66
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..0..0..1. .0..0..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .1..0..0..0
..0..0..1..0. .0..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0
..1..0..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .0..0..0..0
..1..1..1..1. .1..0..0..0. .0..0..1..1. .1..1..0..1. .1..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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