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A200891
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Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.
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1
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114, 1691, 11472, 50995, 173606, 491533, 1215616, 2710413, 5567530, 10700151, 19461872, 33793071, 56398174, 90957305, 142375936, 217076281, 323334306, 471666355, 675269520, 950520011, 1317533910, 1800794821, 2429853056
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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) = (1/315)*n^8 + (134/315)*n^7 + (21/5)*n^6 + (571/36)*n^5 + (1841/60)*n^4 + (6047/180)*n^3 + (26603/1260)*n^2 + (299/42)*n + 1.
G.f.: x*(114 + 665*x + 357*x^2 - 953*x^3 - 37*x^4 - 47*x^5 + 37*x^6 - 9*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
..3....2....2....0....0....3....3....1....1....3....1....3....2....0....0....3
..1....3....0....3....1....0....0....1....3....3....3....3....1....0....0....0
..1....3....3....3....3....0....0....0....3....3....3....1....2....1....3....1
..3....3....3....3....3....3....0....3....0....0....3....0....2....1....3....1
..3....2....3....3....2....3....1....3....1....0....3....0....2....1....0....2
..0....0....0....2....0....1....1....2....3....1....2....1....0....3....2....2
..2....0....1....0....1....0....1....1....3....1....1....1....1....3....2....2
..2....2....1....2....1....0....3....3....2....2....2....3....3....2....2....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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