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A235510
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Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise.
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2
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16, 58, 209, 746, 2660, 9476, 33753, 120216, 428160, 1524918, 5431081, 19343086, 68891428, 245360464, 873864257, 3112313708, 11084669648, 39478636370, 140605248417, 500773018002, 1783529550852, 6352134688572, 22623463167433
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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) = 4*a(n-1) - 6*a(n-3) + a(n-4) + 2*a(n-5).
G.f.: x*(16 - 6*x - 23*x^2 + 6*x^3 + 8*x^4) / ((1 - x)^2*(1 + x)*(1 - 3*x - 2*x^2)).
a(n) = (1/544)*(-221 - 68*(-1)^n + 2^(-1-n)*((2533-611*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(2533+611*sqrt(17))) - 68*(1+n)).
(End)
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EXAMPLE
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Some solutions for n=4:
..1..1....1..1....1..0....0..0....1..0....0..1....1..0....0..1....1..0....0..0
..1..0....0..1....0..0....1..1....1..1....1..1....1..0....1..0....1..1....0..0
..0..1....0..1....1..1....1..0....1..0....0..0....1..1....1..1....0..0....0..1
..1..1....0..1....1..0....1..0....1..1....1..0....1..0....0..0....1..1....1..1
..0..0....0..1....1..0....1..0....1..0....0..1....0..0....1..1....1..1....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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