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A208946
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Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
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2
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5, 22, 57, 122, 223, 366, 563, 820, 1143, 1544, 2029, 2604, 3281, 4066, 4965, 5990, 7147, 8442, 9887, 11488, 13251, 15188, 17305, 19608, 22109, 24814, 27729, 30866, 34231, 37830, 41675, 45772, 50127, 54752, 59653, 64836, 70313, 76090, 82173, 88574
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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) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
Empirical g.f.: x*(5 + 7*x + 6*x^2 + 7*x^3 - x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Mar 07 2018
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EXAMPLE
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Some solutions for n=5:
-5 -3 -3 -3 -5 -3 -5 -4 -3 -4 -4 -4 -4 -4 -5 -3
2 0 -3 3 5 4 -5 2 5 1 0 1 0 -3 1 0
4 2 1 -1 0 -2 5 1 -2 -1 -1 -2 3 3 2 5
-1 1 5 1 0 1 5 1 0 4 5 5 1 4 2 -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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