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A208997
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Number of 6-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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5, 51, 253, 874, 2354, 5404, 11010, 20553, 35781, 58971, 92851, 140818, 206798, 295528, 412352, 563577, 756175, 998245, 1298615, 1667392, 2115476, 2655216, 3299792, 4064019, 4963585, 6015983, 7239629, 8654930, 10283232, 12148080
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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-2) + 2*a(n-3) - 3*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-8) + 4*a(n-9) + 4*a(n-10) + a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) + 2*a(n-16) + 2*a(n-17) - a(n-19).
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EXAMPLE
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Some solutions for n=6:
-3 -4 -5 -3 -2 -3 -4 -4 -4 -4 -4 -3 -5 -4 -2 -2
0 1 1 -3 -2 2 1 -1 1 0 2 1 1 2 -1 -2
4 -2 6 1 1 -2 -2 4 1 5 3 -2 -1 0 1 2
1 0 0 3 0 -1 4 2 2 3 -1 3 5 -2 -1 1
0 3 -2 4 2 1 1 -2 1 -2 1 -1 2 3 4 1
-2 2 0 -2 1 3 0 1 -1 -2 -1 2 -2 1 -1 0
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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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