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A208598
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Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
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2
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6, 23, 60, 125, 226, 371, 568, 825, 1150, 1551, 2036, 2613, 3290, 4075, 4976, 6001, 7158, 8455, 9900, 11501, 13266, 15203, 17320, 19625, 22126, 24831, 27748, 30885, 34250, 37851, 41696, 45793, 50150, 54775, 59676, 64861, 70338, 76115, 82200, 88601
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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) = (4/3)*n^3 + 2*n^2 + (5/3)*n + 1.
G.f.: x*(6 - x + 4*x^2 - x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
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EXAMPLE
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Some solutions for n=4:
-3 -4 -3 -3 -4 -2 -2 -3 -4 -2 -3 -1 -4 -3 -4 -4
1 -2 4 3 0 0 0 -1 1 -2 4 -1 2 -1 1 -1
4 2 0 -3 3 -2 0 3 1 4 -1 2 -2 4 0 3
-2 4 -1 3 1 4 2 1 2 0 0 0 4 0 3 2
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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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