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A299366
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 23, 42, 1, 1, 127, 125, 125, 127, 1, 1, 389, 420, 1157, 420, 389, 1, 1, 1192, 1943, 8134, 8134, 1943, 1192, 1, 1, 3645, 9012, 66668, 107653, 66668, 9012, 3645, 1, 1, 11161, 42321, 564283, 1640199, 1640199, 564283, 42321
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OFFSET
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1,5
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COMMENTS
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Table starts
.1.....1......1........1..........1.............1...............1
.1.....5.....13.......42........127...........389............1192
.1....13.....23......125........420..........1943............9012
.1....42....125.....1157.......8134.........66668..........564283
.1...127....420.....8134.....107653.......1640199........25838859
.1...389...1943....66668....1640199......45416563......1301827631
.1..1192...9012...564283...25838859....1301827631.....67756659422
.1..3645..42321..4792366..404080073...37042505019...3508332244817
.1.11161.205597.41273307.6401182687.1066728270636.183583736926115
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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) +5*a(n-2) +4*a(n-3)
k=3: [order 12] for n>14
k=4: [order 46] for n>48
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0
..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..1..1..0. .1..1..1..1. .1..1..1..1. .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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