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A005513 Number of n-bead bracelets (turn over necklaces) with 6 red beads.
(Formerly M3311)
+0
3
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)
OFFSET

6,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

LINKS

Index entries for sequences related to bracelets

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

FORMULA

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.rs), Feb 28 2007

MATHEMATICA

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

CROSSREFS

Sequence in context: A054599 A095755 A164123 this_sequence A025619 A093210 A133600

Adjacent sequences: A005510 A005511 A005512 this_sequence A005514 A005515 A005516

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Sequence extended and description corrected by Christian G. Bower (bowerc(AT)usa.net)

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Last modified December 10 00:48 EST 2009. Contains 170565 sequences.


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