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A223962
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Number of 2 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
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1
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16, 85, 295, 805, 1876, 3906, 7470, 13365, 22660, 36751, 57421, 86905, 127960, 183940, 258876, 357561, 485640, 649705, 857395, 1117501, 1440076, 1836550, 2319850, 2904525, 3606876, 4445091, 5439385, 6612145, 7988080, 9594376
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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 + (7/48)*n^5 + (157/144)*n^4 + (59/16)*n^3 + (425/72)*n^2 + (25/6)*n + 1.
G.f.: x*(16 - 27*x + 36*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + 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..0..1....1..2..3....0..0..3....3..3..3....0..0..1....1..1..2....0..0..3
..0..0..3....2..2..3....3..3..3....3..3..3....0..2..3....1..2..3....0..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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