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A200877
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Number of 0..n arrays x(0..8) of 9 elements without any interior element greater than both neighbors or less than both neighbors.
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1
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110, 1523, 9858, 42479, 141688, 395929, 971416, 2156867, 4424298, 8509105, 15512938, 27033149, 45322876, 73486107, 115712352, 177555837, 266264422, 391163735, 564102306, 799963779, 1117252576, 1538759685, 2092315544
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OFFSET
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1,1
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COMMENTS
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Row 7 of A200871.
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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) = (1/181440)*n^9 + (131/20160)*n^8 + (8893/30240)*n^7 + (4621/1440)*n^6 + (118933/8640)*n^5 + (83957/2880)*n^4 + (763489/22680)*n^3 + (36343/1680)*n^2 + (9169/1260)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(110 + 423*x - 422*x^2 - 766*x^3 + 848*x^4 - 246*x^5 + 90*x^6 - 44*x^7 + 10*x^8 - x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)
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EXAMPLE
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Some solutions for n=3
..3....3....3....3....3....0....2....2....3....2....3....3....1....1....2....2
..0....0....0....1....3....0....2....2....3....3....3....1....2....1....2....0
..0....0....0....1....3....2....1....0....3....3....3....1....2....1....1....0
..0....2....1....1....2....2....0....0....2....3....3....1....3....3....1....0
..3....2....3....1....1....2....0....2....2....3....1....3....3....3....0....0
..3....1....3....3....1....2....1....2....1....2....1....3....3....2....0....0
..3....0....3....3....0....2....2....0....1....0....1....3....2....1....0....0
..2....0....2....2....0....1....3....0....1....0....1....3....2....0....1....0
..0....1....2....1....2....1....3....2....1....1....3....2....3....0....3....3
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CROSSREFS
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Sequence in context: A231967 A232339 A358256 * A205348 A008450 A163729
Adjacent sequences: A200874 A200875 A200876 * A200878 A200879 A200880
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Nov 23 2011
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STATUS
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approved
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