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A208996
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Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.
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1
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3, 17, 59, 159, 351, 683, 1207, 1989, 3099, 4623, 6647, 9277, 12615, 16787, 21913, 28137, 35597, 44455, 54867, 67015, 81071, 97237, 115701, 136685, 160395, 187071, 216937, 250251, 287255, 328227, 373425, 423147, 477667, 537303, 602347, 673135
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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) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 3*a(n-5) - 3*a(n-6) - a(n-7) + 4*a(n-8) - a(n-9) - 2*a(n-10) + a(n-11).
Empirical g.f.: x*(3 + 11*x + 22*x^2 + 36*x^3 + 39*x^4 + 32*x^5 + 25*x^6 + 14*x^7 - x^9 + x^10) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jul 07 2018
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EXAMPLE
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Some solutions for n=6:
-5 -3 -5 -5 -3 -5 -1 -3 -3 -3 -3 -5 -2 -4 -1 -4
-1 -1 -2 1 1 1 0 2 -2 1 -3 0 -1 -1 0 -4
2 2 4 4 2 1 -1 0 0 -3 -1 4 -2 0 -1 0
4 1 3 0 0 4 2 -1 3 2 4 3 3 4 0 6
0 1 0 0 0 -1 0 2 2 3 3 -2 2 1 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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