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A221597
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Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.
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1
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32, 139, 342, 651, 1068, 1593, 2226, 2967, 3816, 4773, 5838, 7011, 8292, 9681, 11178, 12783, 14496, 16317, 18246, 20283, 22428, 24681, 27042, 29511, 32088, 34773, 37566, 40467, 43476, 46593, 49818, 53151, 56592, 60141, 63798, 67563, 71436, 75417, 79506
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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) = 54*n^2 - 69*n + 63 for n>2.
G.f.: x*(32 + 43*x + 21*x^2 + 10*x^3 + 2*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
(End)
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EXAMPLE
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Some solutions for n=6:
..2....3....6....1....6....5....4....0....1....4....3....0....0....5....1....5
..3....3....6....1....5....5....5....1....2....3....4....0....1....5....2....4
..5....5....6....2....6....6....4....2....5....4....4....3....6....0....4....1
..5....5....5....1....4....2....3....3....4....4....1....2....5....0....5....2
..6....5....4....2....4....3....4....2....3....5....2....1....5....0....6....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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