The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324514 Number of aperiodic permutations of {1..n}. 6
 1, 0, 3, 16, 115, 660, 5033, 39936, 362718, 3624920, 39916789, 478953648, 6227020787, 87177645996, 1307674338105, 20922779566080, 355687428095983, 6402373519409856, 121645100408831981, 2432902004460734000, 51090942171698415483, 1124000727695858073380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A permutation is defined to be aperiodic if every cyclic rotation of {1..n} acts on the cycle decomposition to produce a different digraph. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA a(n) = A306669(n) * n. a(n) = Sum_{d|n} mu(n/d)*(n/d)^d*d!. - Andrew Howroyd, Aug 19 2019 EXAMPLE The a(4) = 16 aperiodic permutations:   (1243) (1324) (1342) (1423)   (2134) (2314) (2413) (2431)   (3124) (3142) (3241) (3421)   (4132) (4213) (4231) (4312) MATHEMATICA Table[Length[Select[Permutations[Range[n]], UnsameQ@@NestList[RotateRight[#/.k_Integer:>If[k==n, 1, k+1]]&, #, n-1]&]], {n, 6}] PROG (PARI) a(n) = sumdiv(n, d, moebius(n/d)*(n/d)^d*d!); \\ Andrew Howroyd, Aug 19 2019 CROSSREFS Cf. A000740, A000939, A027375, A061417, A079128, A086675, A192332, A323860, A323867, A323869. Cf. A306669, A324461, A324462, A324512, A324513, A324514. Sequence in context: A074523 A329113 A042437 * A334786 A159606 A211210 Adjacent sequences:  A324511 A324512 A324513 * A324515 A324516 A324517 KEYWORD nonn AUTHOR Gus Wiseman, Mar 04 2019 EXTENSIONS Terms a(10) and beyond from Andrew Howroyd, Aug 19 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 03:31 EST 2020. Contains 338943 sequences. (Running on oeis4.)