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A208947
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Number of 5-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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1
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8, 68, 274, 766, 1722, 3376, 6004, 9928, 15514, 23178, 33378, 46624, 63464, 84496, 110366, 141766, 179426, 224132, 276712, 338040, 409034, 490662, 583934, 689912, 809696, 944436, 1095330, 1263622, 1450594, 1657584, 1885972, 2137184, 2412690
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OFFSET
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1,1
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COMMENTS
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Row 5 of A208945.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-6) - 2*a(n-7) + 3*a(n-8) - 3*a(n-9) + a(n-10).
Empirical g.f.: 2*x*(4 + 22*x + 47*x^2 + 66*x^3 + 63*x^4 + 48*x^5 + 21*x^6 + 6*x^7 - x^8) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 07 2018
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EXAMPLE
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Some solutions for n=5:
-5 -3 -4 -4 -5 -5 -5 -5 -3 -4 -5 -5 -4 -5 -2 -4
0 2 2 2 -5 4 5 -5 1 -2 4 3 1 -3 4 0
5 -2 3 -2 3 -2 -1 3 -2 2 2 3 3 2 -1 5
-2 4 2 5 5 2 -4 2 5 5 1 0 -2 1 0 1
2 -1 -3 -1 2 1 5 5 -1 -1 -2 -1 2 5 -1 -2
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CROSSREFS
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Cf. A208945.
Sequence in context: A250258 A192091 A050841 * A296670 A263477 A249390
Adjacent sequences: A208944 A208945 A208946 * A208948 A208949 A208950
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Mar 03 2012
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STATUS
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approved
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