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Search: id:A005513
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| A005513 |
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Number of n-bead bracelets (turn over necklaces) with 6 red beads.
(Formerly M3311)
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+0
3
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| 1, 1, 4, 7, 16, 26, 50, 76, 126, 185, 280, 392, 561, 756, 1032, 1353, 1782, 2277, 2920, 3652, 4576, 5626, 6916, 8372, 10133, 12103, 14448, 17063, 20128, 23528, 27474, 31824, 36822, 42315, 48564, 55404, 63133, 71554, 81004
(list; graph; listen)
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OFFSET
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6,3
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REFERENCES
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S. J. Cyvin et al., Polygonal systems including the corannulene ... homologs ..., Z. Naturforsch., 52a (1997), 867-873.
W. D. Hoskins and Anne Penfold Street, Twills on a given number of harnesses, J. Austral. Math. Soc. Ser. A 33 (1982), no. 1, 1-15.
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LINKS
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Index entries for sequences related to bracelets
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
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FORMULA
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S. J. Cyvin et al. give a g.f.
G.f.: (x^6/12)*(1/(1-x)^6+4/(1-x^2)^3+2/(1-x^3)^2+3/((1-x)^2*(1-x^2)^2)+2/(1-x^6)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 28 2007
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MATHEMATICA
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k = 6; Table[(Apply[Plus, Map[EulerPhi[ # ]Binomial[n/#, k/# ] &, Divisors[GCD[n, k]]]]/n + Binomial[If[OddQ[n], n - 1, n - If[OddQ[k], 2, 0]]/2, If[OddQ[k], k - 1, k]/2])/2, {n, k, 50}] - Robert A. Russell (russell(AT)post.harvard.edu), Sep 27 2004
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CROSSREFS
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Adjacent sequences: A005510 A005511 A005512 this_sequence A005514 A005515 A005516
Sequence in context: A067398 A054599 A095755 this_sequence A025619 A093210 A133600
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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Sequence extended and description corrected by Christian G. Bower (bowerc(AT)usa.net)
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