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Search: id:A005514
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| A005514 |
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Number of n-bead bracelets (turn over necklaces) with 8 red beads.
(Formerly M3801)
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+0
4
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| 1, 1, 5, 10, 29, 57, 126, 232, 440, 750, 1282, 2052, 3260, 4950, 7440, 10824, 15581, 21879, 30415, 41470, 56021, 74503, 98254, 127920, 165288, 211276, 268228, 337416, 421856, 523260, 645456, 790704, 963793, 1167645, 1408185
(list; graph; listen)
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OFFSET
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8,3
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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; 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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F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
Index entries for sequences related to bracelets
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FORMULA
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S. J. Cyvin et al. give a g.f.
G.f.: x^8/16*(1/(1 - x)^8 + 4/(1 - x^8) + 5/(1 - x^2)^4 + 2/(1 - x^4)^2 + 4/(1 - x)^2/(1 - x^2)^3) = x^8*(2*x^10 - 3*x^9 + 7*x^8 - 6*x^7 + 7*x^6 - 2*x^5 + 2*x^4 - 2*x^3 + 5*x^2 - 3*x + 1)/(1 - x)^8/(1 + x)^4/(1 + x^2)^2/(1 + x^4). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 17 2002
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MATHEMATICA
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k = 8; 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: A005511 A005512 A005513 this_sequence A005515 A005516 A005517
Sequence in context: A105862 A093029 A105505 this_sequence A069921 A053818 A133629
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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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