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A227269
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T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of three or less, with rows and columns of the latter in lexicographically nondecreasing order
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6
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2, 3, 3, 4, 8, 4, 5, 16, 16, 5, 6, 30, 49, 30, 6, 7, 54, 132, 132, 54, 7, 8, 93, 341, 513, 341, 93, 8, 9, 153, 836, 1949, 1949, 836, 153, 9, 10, 241, 1934, 7131, 10906, 7131, 1934, 241, 10, 11, 365, 4232, 24496, 59952, 59952, 24496, 4232, 365, 11, 12, 534, 8804, 78761
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OFFSET
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1,1
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COMMENTS
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Table starts
..2...3....4......5.......6.........7..........8............9............10
..3...8...16.....30......54........93........153..........241...........365
..4..16...49....132.....341.......836.......1934.........4232..........8804
..5..30..132....513....1949......7131......24496........78761........238146
..6..54..341...1949...10906.....59952.....311644......1513042.......6877791
..7..93..836...7131...59952....498772....3954995.....29333871.....203340009
..8.153.1934..24496..311644...3954995...48265519....553278547....5925354448
..9.241.4232..78761.1513042..29333871..553278547...9879827545..165189287060
.10.365.8804.238146.6877791.203340009.5925354448.165189287060.4332146485870
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 1*n + 1
k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (47/12)*n - 1
k=3: [polynomial of degree 9] for n>3
k=4: [polynomial of degree 19] for n>7
k=5: [polynomial of degree 39] for n>15
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EXAMPLE
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Some solutions for n=4 k=4
..1..1..1..1....1..1..0..0....1..1..0..0....1..1..1..1....1..1..0..0
..1..0..1..1....1..1..1..0....1..1..1..1....1..1..1..0....1..0..0..0
..1..1..0..1....1..1..1..0....1..1..1..1....1..1..0..0....1..0..0..0
..1..1..0..1....0..1..1..0....1..0..0..0....1..1..1..0....1..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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