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A228754
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T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.
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12
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1, 1, 2, 2, 3, 4, 3, 9, 8, 8, 5, 20, 39, 21, 16, 8, 50, 126, 168, 55, 32, 13, 119, 482, 780, 723, 144, 64, 21, 289, 1712, 4599, 4808, 3111, 377, 128, 34, 696, 6277, 24246, 43862, 29608, 13386, 987, 256, 55, 1682, 22700, 134440, 342207, 418370, 182288, 57597, 2584, 512
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OFFSET
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1,3
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COMMENTS
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Table starts
...1....1......2.......3.........5...........8...........13.............21
...2....3......9......20........50.........119..........289............696
...4....8.....39.....126.......482........1712.........6277..........22700
...8...21....168.....780......4599.......24246.......134440.........728537
..16...55....723....4808.....43862......342207......2876170.......23326164
..32..144...3111...29608....418370.....4823826.....61534448......746135864
..64..377..13386..182288...3990739....67970044...1316714732....23857469157
.128..987..57597.1122240..38067290...957616341..28177227352...762713002760
.256.2584.247827.6908896.363121586.13491214832.602998827928.24382157716612
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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)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -3*a(n-2)
k=4: a(n) = 8*a(n-1) -12*a(n-2) +4*a(n-3)
k=5: a(n) = 13*a(n-1) -36*a(n-2) +29*a(n-3) -5*a(n-4) for n>5
k=6: a(n) = 21*a(n-1) -112*a(n-2) +217*a(n-3) -157*a(n-4) +36*a(n-5) for n>6
k=7: [order 7] for n>9
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2) +a(n-3)
n=3: a(n) = 2*a(n-1) +6*a(n-2) -a(n-4)
n=4: [order 8]
n=5: [order 13]
n=6: [order 21]
n=7: [order 34]
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..1..0....1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0
..0..0..0..1....1..0..0..0....1..0..0..0....0..1..0..0....1..0..0..1
..0..0..0..0....1..0..0..1....0..0..0..0....0..0..0..1....0..1..0..1
..0..0..0..1....0..0..0..0....0..1..0..0....0..1..0..0....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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