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A298280
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 129, 64, 3, 5, 236, 873, 873, 236, 5, 8, 888, 6013, 10679, 6013, 888, 8, 13, 3336, 41437, 136006, 136006, 41437, 3336, 13, 21, 12512, 285280, 1735247, 3214459, 1735247, 285280, 12512, 21, 34, 46928, 1964290
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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.....4.......18.........64...........236.............888..............3336
..1....18......129........873..........6013...........41437............285280
..2....64......873......10679........136006.........1735247..........22110710
..3...236.....6013.....136006.......3214459........75989207........1794078025
..5...888....41437....1735247......75989207......3328434344......145597697355
..8..3336...285280...22110710....1794078025....145597697355....11799327975543
.13.12512..1964290..281745241...42359577845...6369396379414...956310372633436
.21.46928.13524686.3590209542.1000164240246.278645510729761.77508769959888329
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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) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4
k=3: [order 10] for n>11
k=4: [order 30] for n>32
k=5: [order 92] for n>96
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..0. .0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..0
..0..1..1..0. .1..1..1..0. .0..1..0..1. .1..0..0..1. .0..1..1..1
..1..0..0..1. .0..1..1..0. .0..1..1..0. .1..1..0..1. .0..1..1..0
..1..0..0..1. .0..0..1..0. .1..1..1..0. .1..0..1..0. .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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