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Search: id:A130293
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| A130293 |
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Number of necklaces of n beads with up to n colours, with cyclic permutation {1,..,n} of the colours taken to be equivalent. |
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+0
1
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| 1, 2, 5, 20, 129, 1316, 16813, 262284, 4783029, 100002024, 2357947701, 61917406672, 1792160394049, 56693913450992, 1946195068379933, 72057594071484456, 2862423051509815809, 121439531097819321972
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For prime n, the sequence seems to be n^(n-2)+n-1.
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FORMULA
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(1/n^2)*Sum_{d|n} d*phi(d)*n^(n/d) from Vladeta Jovovic (vladeta(AT)EUnet.yu), Aug 14 2007, Aug 24 2007
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EXAMPLE
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The 5 necklaces for n=3 are: 000, 001, 002, 012 and 021.
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MATHEMATICA
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tor8={}; ru8=Thread[ i_ ->Table[ Mod[i+k, 8], {k, 8}]]; Do[idi=IntegerDigits[k, 8, 8]; try= Function[w, First[temp=Union[Join @@(Table[RotateRight[w, k], {k, 8}]/.#&)/@ ru8]]][idi]; If[idi===try, tor8=Flatten[ {tor8, {{Length[temp], idi}}}, 1] ], {k, 0, 8^8-1}];
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CROSSREFS
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Cf. A002075-A002076.
Cf. A056665.
Sequence in context: A012321 A012519 A076795 this_sequence A006366 A012317 A118181
Adjacent sequences: A130290 A130291 A130292 this_sequence A130294 A130295 A130296
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 06 2007, Aug 14 2007
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