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A221686
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Number of 0..n arrays of length 7 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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64, 320, 844, 1692, 2856, 4326, 6102, 8184, 10572, 13266, 16266, 19572, 23184, 27102, 31326, 35856, 40692, 45834, 51282, 57036, 63096, 69462, 76134, 83112, 90396, 97986, 105882, 114084, 122592, 131406, 140526, 149952, 159684, 169722, 180066, 190716
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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) = 153*n^2 - 213*n + 96 for n>3.
G.f.: 2*x*(32 + 64*x + 38*x^2 + 28*x^3 - 4*x^4 - 5*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(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....1....0....0....1....0....1....0....0....0....0....0....0....1....1
..2....1....1....1....2....5....0....2....3....1....4....3....2....1....3....2
..3....1....0....1....1....5....0....3....2....1....3....3....3....1....2....2
..0....0....4....0....4....5....5....5....3....2....5....4....5....3....1....3
..1....2....5....2....4....4....5....6....4....4....4....3....5....4....6....4
..2....1....5....3....3....5....4....6....3....4....4....2....4....3....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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