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A262759
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T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with each row divisible by 5 and each column divisible by 7, read as a binary number with top and left being the most significant bits.
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13
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2, 4, 3, 7, 9, 5, 13, 17, 25, 10, 26, 37, 49, 100, 19, 52, 107, 129, 319, 361, 37, 103, 321, 709, 1645, 1345, 1369, 74, 205, 865, 4953, 16450, 8605, 6193, 5476, 147, 410, 2449, 16705, 243220, 135595, 52993, 39751, 21609, 293, 820, 7299, 73345, 1614175
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OFFSET
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1,1
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COMMENTS
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Table starts
...2......4.......7.......13........26.........52........103.........205
...3......9......17.......37.......107........321........865........2449
...5.....25......49......129.......709.......4953......16705.......73345
..10....100.....319.....1645.....16450.....243220....1614175....15350125
..19....361....1345.....8605....135595....3051121...31840777...475175089
..37...1369....6193....52993...1635877...71515801.1252506169.32264365249
..74...5476...39751...658381..37426418.3270912532
.147..21609..229841..5747701.595006235
.293..85849.1339569.51979793
.586.343396.8663743
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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) +a(n-3) -2*a(n-4)
k=2: a(n) = 4*a(n-1) +9*a(n-3) -36*a(n-4) -8*a(n-6) +32*a(n-7)
Empirical for row n:
n=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
n=2: [order 8]
n=3: [order 17]
n=4: [order 16]
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EXAMPLE
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Some solutions for n=4, k=4
..1..0..0..0..1..1....1..1..1..1..0..0....1..0..0..0..1..1....1..1..1..1..0..0
..1..0..1..0..0..0....1..1..1..1..0..0....1..0..1..1..0..1....1..1..0..0..1..0
..1..0..0..0..1..1....1..1..1..1..0..0....1..0..1..0..0..0....1..0..1..1..0..1
..1..1..1..1..0..0....0..1..1..0..0..1....1..1..1..1..0..0....1..0..0..0..1..1
..1..1..0..1..1..1....0..1..1..0..0..1....1..1..0..0..1..0....1..0..1..1..0..1
..1..1..1..1..0..0....0..1..1..0..0..1....1..1..0..1..1..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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