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A317222
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 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, 25, 25, 2, 3, 98, 133, 98, 3, 5, 383, 929, 929, 383, 5, 8, 1493, 6134, 11378, 6134, 1493, 8, 13, 5824, 40873, 133874, 133874, 40873, 5824, 13, 21, 22717, 272012, 1580822, 2762836, 1580822, 272012, 22717, 21, 34, 88609, 1810626
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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.......25.........98..........383............1493..............5824
..1....25......133........929.........6134...........40873............272012
..2....98......929......11378.......133874.........1580822..........18667993
..3...383.....6134.....133874......2762836........57448875........1193567097
..5..1493....40873....1580822.....57448875......2106680104.......77171164500
..8..5824...272012...18667993...1193567097.....77171164500.....4981964443017
.13.22717..1810626..220464927..24804953660...2827889481366...321779228843527
.21.88609.12051365.2603595850.515450451064.103616727948480.20780911115253208
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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) +3*a(n-2) +2*a(n-3)
k=3: [order 9] for n>10
k=4: [order 28] for n>29
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..0. .0..1..0..0
..1..0..1..1. .1..1..0..1. .1..0..0..0. .1..1..1..0. .0..1..0..1
..1..0..0..1. .1..0..1..0. .1..0..1..0. .0..1..0..0. .1..1..0..0
..0..0..1..1. .0..0..1..1. .1..1..0..0. .1..0..1..0. .1..1..0..0
..1..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..1..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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