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A221525
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Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more.
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1
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0, 6, 94, 536, 1940, 5368, 12458, 25544, 47776, 83240, 137078, 215608, 326444, 478616, 682690, 950888, 1297208, 1737544, 2289806, 2974040, 3812548, 4830008, 6053594, 7513096, 9241040, 11272808, 13646758, 16404344, 19590236, 23252440
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OFFSET
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1,2
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COMMENTS
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Row 5 of A221524.
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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) = 1*n^5 - 1*n^4 - 10*n^3 + 38*n^2 - 60*n + 40 for n>2.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: 2*x^2*(3 + 29*x + 31*x^2 + 7*x^3 - 11*x^4 + 2*x^5 - x^6) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.
(End)
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EXAMPLE
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Some solutions for n=6:
..5....2....6....1....5....4....4....0....4....1....3....6....2....1....2....2
..2....0....0....5....1....0....2....2....0....4....1....1....6....4....0....6
..5....4....0....2....6....2....2....5....5....5....1....2....5....1....4....3
..5....6....6....2....0....2....0....4....0....2....4....0....0....3....2....4
..3....3....0....0....5....0....6....6....3....6....1....3....4....6....4....0
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CROSSREFS
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Cf. A221524.
Sequence in context: A033935 A218682 A078103 * A321073 A198257 A296820
Adjacent sequences: A221522 A221523 A221524 * A221526 A221527 A221528
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Jan 19 2013
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STATUS
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approved
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