|
Search: id:A005513
|
|
|
| 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)
|
|
|
Search completed in 0.002 seconds
|
