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A251201
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements less than the absolute difference of its antidiagonal elements
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9
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10, 25, 25, 64, 86, 64, 164, 310, 310, 164, 421, 1135, 1654, 1135, 421, 1081, 4172, 8976, 8976, 4172, 1081, 2776, 15353, 49104, 73170, 49104, 15353, 2776, 7129, 56519, 268638, 599869, 599869, 268638, 56519, 7129, 18308, 208082, 1470646, 4923412
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OFFSET
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1,1
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COMMENTS
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Table starts
....10......25........64.........164...........421............1081
....25......86.......310........1135..........4172...........15353
....64.....310......1654........8976.........49104..........268638
...164....1135......8976.......73170........599869.........4923412
...421....4172.....49104......599869.......7392190........91120318
..1081...15353....268638.....4923412......91120318......1688254298
..2776...56519...1470646....40413851....1123772109.....31288421074
..7129..208082...8050116...331748759...13857491196....579864211963
.18308..766105..44068836..2723267431..170891121600..10746714294838
.47017.2820622.241240750.22354871755.2107379861537.199169443650957
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) -a(n-4)
k=2: a(n) = 2*a(n-1) +7*a(n-2) -a(n-3) -7*a(n-4) -a(n-5) for n>6
k=3: [order 9] for n>10
k=4: [order 14] for n>16
k=5: [order 22] for n>25
k=6: [order 35] for n>39
k=7: [order 56] for n>61
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EXAMPLE
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Some solutions for n=4 k=4
..1..1..1..0..1....1..0..1..1..0....1..1..0..1..1....1..0..1..0..1
..1..0..1..1..0....0..1..1..1..1....0..1..1..1..0....0..1..0..1..0
..0..1..0..1..1....1..0..1..1..1....1..1..0..1..1....1..1..1..1..1
..1..0..1..0..1....1..1..1..1..0....0..1..1..1..0....1..1..0..1..1
..0..1..1..1..1....1..1..0..1..1....1..0..1..1..1....1..1..1..1..1
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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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