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A200889
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Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.
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1
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37, 292, 1268, 3985, 10213, 22736, 45648, 84681, 147565, 244420, 388180, 595049, 884989, 1282240, 1815872, 2520369, 3436245, 4610692, 6098260, 7961569, 10272053, 13110736, 16569040, 20749625, 25767261, 31749732, 38838772, 47191033, 56979085
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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) = (2/45)*n^6 + (19/15)*n^5 + (217/36)*n^4 + (71/6)*n^3 + (2057/180)*n^2 + (27/5)*n + 1.
G.f.: x*(37 + 33*x + x^2 - 54*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=3
..1....0....3....0....2....2....1....0....1....3....2....3....2....2....3....2
..0....1....1....3....1....3....1....0....1....0....2....3....3....1....1....2
..1....2....0....3....3....3....2....0....0....1....1....0....3....0....3....2
..3....2....1....0....3....2....2....1....1....2....0....0....1....0....3....2
..3....2....2....0....1....2....3....2....2....2....1....2....0....2....2....1
..3....3....2....3....1....0....3....2....2....1....2....2....3....3....2....0
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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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