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A223919
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Number of 2 X n 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.
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3
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6, 36, 158, 548, 1600, 4102, 9503, 20299, 40570, 76704, 138348, 239630, 400700, 649642, 1024813, 1577669, 2376142, 3508636, 5088714, 7260552, 10205240, 14148014, 19366507, 26200111, 35060546, 46443736, 60943096, 79264338
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OFFSET
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1,1
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COMMENTS
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Row 2 of A223918.
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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) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (259/480)*n^4 + (173/144)*n^3 + (4877/2520)*n^2 + (481/420)*n + 1.
Conjectures from Colin Barker, Feb 23 2018: (Start)
G.f.: x*(6 - 18*x + 50*x^2 - 82*x^3 + 88*x^4 - 62*x^5 + 29*x^6 - 8*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
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EXAMPLE
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Some solutions for n=3:
..1..2..0....0..0..2....1..0..0....0..0..0....0..1..1....1..2..0....0..1..0
..1..2..0....0..0..2....1..0..0....1..1..0....0..2..1....1..2..2....1..1..2
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CROSSREFS
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Cf. A223918.
Sequence in context: A224149 A055404 A223946 * A263952 A281394 A225380
Adjacent sequences: A223916 A223917 A223918 * A223920 A223921 A223922
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Mar 29 2013
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STATUS
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approved
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