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A219472
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Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 2 X n array.
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1
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10, 23, 68, 211, 547, 1248, 2663, 5432, 10666, 20206, 36984, 65512, 112528, 187831, 305340, 484415, 751481, 1141999, 1702831, 2495049, 3597241, 5109370, 7157245, 9897666, 13524308, 18274412, 24436354, 32358166, 42457086, 55230217, 71266378
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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) = (1/13440)*n^8 + (1/10080)*n^7 + (1/576)*n^6 + (119/720)*n^5 - (9659/5760)*n^4 + (18247/1440)*n^3 - (50047/2016)*n^2 + (6437/840)*n + 13 for n>3.
G.f.: x*(10 - 67*x + 221*x^2 - 413*x^3 + 424*x^4 - 153*x^5 - 91*x^6 + 35*x^7 + 124*x^8 - 129*x^9 + 49*x^10 - 7*x^11) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.
(End)
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EXAMPLE
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Some solutions for n=3:
..2..2..2....2..2..2....0..0..1....1..1..1....2..2..2....1..1..1....0..0..1
..2..2..2....2..1..1....1..0..0....1..1..1....2..0..0....1..2..2....1..3..3
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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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