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A223835
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Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
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1
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16, 86, 255, 596, 1240, 2388, 4325, 7436, 12222, 19316, 29499, 43716, 63092, 88948, 122817, 166460, 221882, 291348, 377399, 482868, 610896, 764948, 948829, 1166700, 1423094, 1722932, 2071539, 2474660, 2938476, 3469620, 4075193, 4762780, 5540466
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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) = (2/15)*n^5 + (1/6)*n^4 + (19/6)*n^3 + (28/3)*n^2 + (126/5)*n - 36 for n>2.
G.f.: x*(16 - 10*x - 21*x^2 + 36*x^3 + 9*x^4 - 18*x^5 + 2*x^6 + 2*x^7) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.
(End)
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EXAMPLE
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Some solutions for n=3:
..1..0..0..0..0....1..1..1..0..0....1..0..0..0..0....0..1..1..0..0
..1..1..1..1..0....1..1..1..0..0....1..1..1..1..0....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..0....1..1..1..1..0....1..1..1..1..1
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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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