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A200874
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Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors or less than both neighbors.
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1
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26, 163, 602, 1673, 3886, 7973, 14932, 26073, 43066, 67991, 103390, 152321, 218414, 305929, 419816, 565777, 750330, 980875, 1265762, 1614361, 2037134, 2545709, 3152956, 3873065, 4721626, 5715711, 6873958, 8216657, 9765838, 11545361
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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) = (1/360)*n^6 + (7/24)*n^5 + (197/72)*n^4 + (185/24)*n^3 + (1667/180)*n^2 + 5*n + 1.
G.f.: x*(26 - 19*x + 7*x^2 - 28*x^3 + 22*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
..2....0....2....0....2....1....2....0....3....0....0....1....3....3....1....1
..0....2....2....3....0....2....1....1....3....2....0....1....3....0....2....3
..0....2....2....3....0....2....1....3....0....3....1....1....2....0....2....3
..0....0....2....2....0....2....2....3....0....3....2....0....2....1....2....2
..0....0....1....2....1....1....2....0....2....3....2....0....3....1....2....2
..0....3....1....3....1....0....1....0....2....1....0....0....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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