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A221677
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Number of 0..2 arrays of length n 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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0, 2, 5, 14, 40, 113, 320, 906, 2565, 7262, 20560, 58209, 164800, 466578, 1320965, 3739886, 10588280, 29977297, 84871040, 240284954, 680289285, 1926019518, 5452902560, 15438133441, 43708091520, 123745352482, 350345021445
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OFFSET
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1,2
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COMMENTS
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Column 2 of A221683.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3).
Empirical g.f.: x^2*(2 + x) / (1 - 2*x - 2*x^2 - x^3). - Colin Barker, Oct 19 2017
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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....1....1....1....1....1....1....0....1....0....1....1....1....0....0....1
..2....1....0....0....1....0....2....2....2....1....2....1....2....2....1....0
..0....1....0....0....1....0....2....2....0....1....0....2....1....2....0....0
..1....0....2....0....2....1....2....0....0....0....0....1....2....1....1....1
..0....1....2....1....2....1....1....0....1....1....0....2....1....0....0....0
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CROSSREFS
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Sequence in context: A296516 A111109 A081908 * A229737 A059505 A159035
Adjacent sequences: A221674 A221675 A221676 * A221678 A221679 A221680
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Jan 22 2013
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STATUS
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approved
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