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A208827
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Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero.
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1
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18, 167, 828, 2821, 7582, 17339, 35288, 65769, 114442, 188463, 296660, 449709, 660310, 943363, 1316144, 1798481, 2412930, 3184951, 4143084, 5319125, 6748302, 8469451, 10525192, 12962105, 15830906, 19186623, 23088772, 27601533, 32793926
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listen;
history;
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OFFSET
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1,1
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COMMENTS
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Row 6 of A208825.
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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) = (22/15)*n^5 + (11/3)*n^4 + (14/3)*n^3 + (13/3)*n^2 + (43/15)*n + 1.
Conjectures from Colin Barker, Jul 07 2018: (Start)
G.f.: x*(18 + 59*x + 96*x^2 - 2*x^3 + 6*x^4 - x^5) / (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>6.
(End)
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EXAMPLE
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Some solutions for n=3:
-3 -3 -3 -2 -2 -3 -3 -2 -3 -3 -3 -3 -2 -3 -3 -2
-1 0 -2 0 -1 -2 -1 -1 0 -3 -1 -1 -1 2 -2 0
3 1 0 0 3 2 0 1 -2 1 0 2 -2 -2 3 1
-2 -1 3 0 0 3 2 -2 -1 3 0 -1 2 -2 2 -2
3 0 3 0 0 -3 -1 2 3 0 3 3 0 2 -1 0
0 3 -1 2 0 3 3 2 3 2 1 0 3 3 1 3
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CROSSREFS
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Cf. A208825.
Sequence in context: A099196 A041618 A055915 * A327792 A071539 A125381
Adjacent sequences: A208824 A208825 A208826 * A208828 A208829 A208830
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Mar 01 2012
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STATUS
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approved
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