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A231070
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T(n,k)=Number of black square subarrays of (n+1)X(k+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
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5
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1, 1, 1, 2, 3, 2, 3, 4, 4, 3, 5, 11, 11, 11, 5, 8, 15, 24, 24, 15, 8, 13, 42, 59, 89, 59, 42, 13, 21, 57, 139, 191, 191, 139, 57, 21, 34, 161, 332, 748, 685, 748, 332, 161, 34, 55, 218, 796, 1573, 2379, 2379, 1573, 796, 218, 55, 89, 617, 1903, 6259, 8357, 13785, 8357
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OFFSET
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1,4
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COMMENTS
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Table starts
..1...1...2....3.....5......8......13.......21.......34........55.........89
..1...3...4...11....15.....42......57......161......218.......617........835
..2...4..11...24....59....139.....332......796.....1903......4563......10934
..3..11..24...89...191....748....1573.....6259....13176.....52497.....110739
..5..15..59..191...685...2379....8357....29493...103842....366761....1295168
..8..42.139..748..2379..13785...43004...253150...793041...4669709...14671984
.13..57.332.1573..8357..43004..223270..1168723..6098749..31928221..167211867
.21.161.796.6259.29493.253150.1168723.10204445.47403200.414060681.1930022303
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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) = 5*a(n-2) -5*a(n-4) +2*a(n-6)
k=3: a(n) = 2*a(n-1) +3*a(n-2) -3*a(n-3) -6*a(n-4) +2*a(n-5) +4*a(n-6) -a(n-7) -a(n-8)
k=4: [order 18, even terms]
k=5: [order 32]
k=6: [order 70, even terms]
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EXAMPLE
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Some solutions for n=4 k=4
..x..0..x..1..x....x..0..x..0..x....x..0..x..1..x....x..0..x..0..x
..1..x..0..x..0....1..x..1..x..1....1..x..0..x..1....0..x..1..x..0
..x..1..x..0..x....x..0..x..0..x....x..1..x..0..x....x..1..x..1..x
..0..x..1..x..1....1..x..1..x..1....0..x..0..x..1....1..x..0..x..1
..x..1..x..0..x....x..0..x..0..x....x..1..x..1..x....x..0..x..0..x
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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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