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A201696
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Number of n X 4 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
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1
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3, 27, 395, 4998, 35390, 167625, 607919, 1826778, 4775228, 11211034, 24167306, 48600665, 92261185, 166831642, 289389192, 484248471, 785251265, 1238574341, 1906133765, 2869671064, 4235613920, 6140811719, 8759254221, 12309889872
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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) = (1/907200)*n^10 + (13/20160)*n^9 + (8321/120960)*n^8 + (97/105)*n^7 - (40969/5400)*n^6 + (22681/960)*n^5 - (11661313/362880)*n^4 - (388097/10080)*n^3 + (4320179/16800)*n^2 - (323861/840)*n + 185.
G.f.: x*(3 - 6*x + 263*x^2 + 1643*x^3 - 1328*x^4 - 4426*x^5 + 5086*x^6 - 1972*x^7 + 1789*x^8 - 1233*x^9 + 185*x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..1..1..2....0..1..1..2....0..1..1..1....0..1..2..2....0..1..2..2
..1..0..0..2....2..1..1..0....2..0..0..0....0..2..0..0....0..2..1..2
..2..2..2..0....2..1..1..0....2..0..0..0....1..0..0..0....2..1..1..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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