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A224001
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Number of 3 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
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1
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27, 157, 476, 1144, 2403, 4614, 8291, 14141, 23109, 36428, 55674, 82826, 120331, 171174, 238953, 327959, 443261, 590796, 777464, 1011228, 1301219, 1657846, 2092911, 2619729, 3253253, 4010204, 4909206, 5970926, 7218219, 8676278
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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) = (1/144)*n^6 + (5/48)*n^5 + (163/144)*n^4 + (85/16)*n^3 + (895/36)*n^2 - (65/12)*n + 3 for n>2.
G.f.: x*(27 - 32*x - 56*x^2 + 164*x^3 - 159*x^4 + 85*x^5 - 32*x^6 + 9*x^7 - x^8) / (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>9.
(End)
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EXAMPLE
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Some solutions for n=3:
..1..2..2....0..1..2....0..1..1....1..2..2....0..0..0....0..0..2....2..2..2
..0..1..2....1..2..2....0..1..2....1..1..2....0..1..2....0..0..0....2..2..2
..1..1..1....2..2..2....0..1..1....1..1..1....0..1..1....0..1..2....1..2..2
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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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