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A299135
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 7 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, 30, 42, 1, 1, 127, 149, 149, 127, 1, 1, 389, 576, 1261, 576, 389, 1, 1, 1192, 2621, 9316, 9316, 2621, 1192, 1, 1, 3645, 12495, 75592, 130924, 75592, 12495, 3645, 1, 1, 11161, 59426, 648807, 1969223, 1969223, 648807, 59426
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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.....30......149........576..........2621...........12495
.1....42....149.....1261.......9316.........75592..........648807
.1...127....576.....9316.....130924.......1969223........31421743
.1...389...2621....75592....1969223......54173918......1576974771
.1..1192..12495...648807...31421743....1576974771.....83518793627
.1..3645..59426..5568411..497341456...45531416012...4394242516518
.1.11161.291819.48528385.7976508449.1330533860979.233738399148294
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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 49] for n>51
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..0..1..1. .0..0..1..1. .0..1..1..1
..0..0..1..0. .1..1..1..1. .0..1..1..0. .0..0..1..1. .0..0..1..1
..0..1..0..0. .0..0..0..1. .0..0..1..1. .1..1..0..0. .0..0..1..0
..0..1..1..1. .0..0..0..0. .0..0..1..1. .1..1..0..0. .1..1..0..0
..0..0..1..0. .1..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..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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