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Search: id:A032279
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| A032279 |
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Number of bracelets (turn over necklaces) of n beads of 2 colors, 5 of them black. |
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+0
3
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| 1, 1, 3, 5, 10, 16, 26, 38, 57, 79, 111, 147, 196, 252, 324, 406, 507, 621, 759, 913, 1096, 1298, 1534, 1794, 2093, 2421, 2793, 3199, 3656, 4152, 4706, 5304, 5967, 6681, 7467, 8311, 9234, 10222, 11298, 12446, 13691, 15015, 16445
(list; graph; listen)
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OFFSET
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5,3
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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.
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LINKS
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Index entries for sequences related to bracelets
C. G. Bower, Transforms (2)
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
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FORMULA
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"DIK[ 5 ]" (necklace, indistinct, unlabeled, 5 parts) transform of 1, 1, 1, 1...
G.f.: (1-x+2*x^3-x^5+x^6)/((1-x)^2*(1-x^2)^2*(1-x^5)).
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MATHEMATICA
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k = 5; 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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PROGRAM
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(PARI) a(n) =(n^4 -10*n^3 +50*n^2 -(110+30*(1-n%2))*n +(144-75*(n%2)+96*(1&(1<<(n%5)))))/240 - Washington Bomfim (webonfim(AT)bol.com.br), Jul 17 2008
(PARI) a(n) = round((n^4 -10*n^3 +50*n^2 -(110+30*(1-n%2))*n) /240 +0.6) - Washington Bomfim (webonfim(AT)bol.com.br), Jul 17 2008
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CROSSREFS
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Sequence in context: A054473 A006168 A037246 this_sequence A070558 A070559 A000990
Adjacent sequences: A032276 A032277 A032278 this_sequence A032280 A032281 A032282
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), N. J. A. Sloane (njas(AT)research.att.com).
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