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A324514
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Number of aperiodic permutations of {1..n}.
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7
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1, 0, 3, 16, 115, 660, 5033, 39936, 362718, 3624920, 39916789, 478953648, 6227020787, 87177645996, 1307674338105, 20922779566080, 355687428095983, 6402373519409856, 121645100408831981, 2432902004460734000, 51090942171698415483, 1124000727695858073380
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OFFSET
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1,3
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COMMENTS
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A permutation is defined to be aperiodic if every cyclic rotation of {1..n} acts on the cycle decomposition to produce a different digraph.
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 16 aperiodic permutations:
(1243) (1324) (1342) (1423)
(2134) (2314) (2413) (2431)
(3124) (3142) (3241) (3421)
(4132) (4213) (4231) (4312)
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MATHEMATICA
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Table[Length[Select[Permutations[Range[n]], UnsameQ@@NestList[RotateRight[#/.k_Integer:>If[k==n, 1, k+1]]&, #, n-1]&]], {n, 6}]
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(n/d)^d*d!); \\ Andrew Howroyd, Aug 19 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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