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A202198
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Number of (n+2) X 6 binary arrays avoiding patterns 001 and 101 in rows and columns.
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1
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756, 2688, 7560, 18144, 38808, 76032, 138996, 240240, 396396, 628992, 965328, 1439424, 2093040, 2976768, 4151196, 5688144, 7671972, 10200960, 13388760, 17365920, 22281480, 28304640, 35626500, 44461872, 55051164, 67662336, 82592928
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/10.
G.f.: 12*x*(63 - 217*x + 385*x^2 - 399*x^3 + 245*x^4 - 83*x^5 + 12*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..1..1..1..1..1....1..1..1..0..0..0....0..1..1..0..0..0....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..0..0..0....0..1..1..0..0..0....1..1..1..1..1..1
..0..1..1..1..0..0....1..1..0..0..0..0....0..1..1..0..0..0....1..1..1..1..1..1
..0..1..1..0..0..0....1..1..0..0..0..0....0..1..1..0..0..0....1..1..1..0..0..0
..0..1..1..0..0..0....1..1..0..0..0..0....0..1..1..0..0..0....0..1..1..0..0..0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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