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A225009
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Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.
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1
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29, 239, 1163, 4166, 12174, 30738, 69498, 144111, 278707, 508937, 885677, 1479452, 2385644, 3730548, 5678340, 8439021, 12277401, 17523187, 24582239, 33949058, 46220570, 62111270, 82469790, 108296955, 140765391, 181240749, 231304609
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OFFSET
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1,1
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (58/45)*n^5 + (35/8)*n^4 + (1507/180)*n^3 + (357/40)*n^2 + (2027/420)*n + 1.
Conjectures from Colin Barker, Sep 05 2018: (Start)
G.f.: x*(29 + 7*x + 63*x^2 - 70*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..1..1..0..0..0..0....1..1..1..1..0..0..0....0..0..0..0..0..0..0
..0..1..1..1..1..0..0....1..1..1..1..1..0..0....1..1..0..0..0..0..0
..1..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..0..0..0..0..0
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CROSSREFS
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Column 7 of A225010.
Sequence in context: A126426 A126425 A224145 * A177419 A142559 A125366
Adjacent sequences: A225006 A225007 A225008 * A225010 A225011 A225012
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Apr 23 2013
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STATUS
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approved
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