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Search: id:A072605
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| A072605 |
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Number of necklaces of n beads and up to n unlabeled (interchangeable) colors. |
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+0
1
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| 1, 2, 4, 13, 50, 270, 1641, 11945, 96784, 887982, 8939051, 99298354, 1195617443, 15619182139, 219049941201, 3293800835940, 52746930894774, 897802366250126, 16167544246362567, 307372573011579188, 6148811682561390279
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Frank Ruskey, Necklaces with Fixed Density
Eric Weisstein's world of Mathematics, Necklaces
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FORMULA
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See Mathematica line.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; neck[li:{__Integer}] := Module[{n, d}, n=Plus@@li; d=n-First[li]; Fold[ #1+(EulerPhi[ #2]*(n/#2)!)/Times@@((li/#2)!)&, 0, Divisors[GCD@@li]]/n]; Table[ Plus@@(neck /@ Partitions[n]), {n, 24}]
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CROSSREFS
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Cf. A052307.
Sequence in context: A005164 A058134 A069730 this_sequence A030953 A030811 A030917
Adjacent sequences: A072602 A072603 A072604 this_sequence A072606 A072607 A072608
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KEYWORD
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easy,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 06 2002
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