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A221685
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Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less, starting with 0.
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1
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32, 113, 241, 418, 636, 891, 1182, 1509, 1872, 2271, 2706, 3177, 3684, 4227, 4806, 5421, 6072, 6759, 7482, 8241, 9036, 9867, 10734, 11637, 12576, 13551, 14562, 15609, 16692, 17811, 18966, 20157, 21384, 22647, 23946, 25281, 26652, 28059, 29502, 30981
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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) = 18*n^2 + 57*n - 99 for n>4.
G.f.: x*(32 + 17*x - 2*x^2 + 2*x^3 - 8*x^4 - 4*x^5 - x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)
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EXAMPLE
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Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....0....1....1....0....1....0....1....0....0....0....1....0....1....0
..3....0....2....5....0....6....3....0....0....1....5....6....0....1....4....4
..4....0....1....5....3....5....4....1....5....5....4....6....0....3....4....5
..3....0....4....2....2....1....2....2....4....4....3....1....2....2....0....2
..2....1....4....2....2....2....3....1....4....3....2....1....3....3....0....3
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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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