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A208601
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Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
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2
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57, 1163, 8671, 39019, 129823, 353333, 833253, 1764925, 3438877, 6267735, 10816499, 17836183, 28300819, 43447825, 64821737, 94321305, 134249953, 187369603, 256957863, 346868579, 461595751, 606340813, 787083277, 1010654741
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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) = (841/180)*n^6 + (841/60)*n^5 + (325/18)*n^4 + (51/4)*n^3 + (949/180)*n^2 + (37/30)*n + 1.
G.f.: x*(57 + 764*x + 1727*x^2 + 750*x^3 + 71*x^4 - 6*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=4:
-4 -2 -4 -4 -4 -3 -3 -4 -2 -4 -4 -3 -3 -3 -4 -4
-2 -2 3 1 -2 2 0 -4 2 -1 2 -1 0 1 2 2
3 1 2 -2 0 0 -1 -2 1 2 -2 0 1 0 -3 -4
1 2 1 0 3 2 2 1 1 -4 1 0 0 1 4 4
-2 -2 -1 2 3 -3 -1 1 -1 3 -3 -1 -2 -2 -4 1
1 1 -1 -1 -3 3 2 4 0 3 2 2 2 1 3 -2
3 2 0 4 3 -1 1 4 -1 1 4 3 2 2 2 3
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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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