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 A141599 Number of difference sets for permutations of [2n] with distinct differences. 6
 1, 2, 4, 24, 288, 3856, 89328, 2755968, 103653120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of all-interval rows for systems with 2n notes in the octave (2n-edo). As determined by direct enumeration up to n=6, a(n) is the number of circular permutations of the integers from 0 to 2n-1 in which all "stepping-on" sequences terminate and one is complete. For example, 07531642 is one of the 24 such permutations for n=4, as starting at 1 and moving to the right by the number of steps indicated gives the complete sequence 1, 6, 3, 4, 5, 2, 7, 0. - Ian Duff, Oct 07 2018 No permutations of the integers from 0 to 2n can generate such a complete sequence. - Ian Duff, Dec 25 2018 LINKS Zack Baker, Properties and Calculations of Constructive Orderings on Z/nZ, Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 4, n. 1, mar. 2019. E. N. Gilbert, Latin squares which contain no repeated digrams, SIAM Rev. 7 1965 189--198. MR0179095 (31 #3346). Mentions this sequence. - N. J. A. Sloane, Mar 15 2014 Milan Gustar, More information Milan Gustar, Programs and data MATHEMATICA A141599[n_] := With[{s = Join[{1}, #[[ ;; n - 1]], {2 n}, #[[n ;; ]]] & /@ Permutations@Range[2, 2 n - 1], mcts = Mod[Differences@Ordering@#, 2 n] &}, Count[mcts /@ s, _?DuplicateFreeQ, 1]]; (* Leo C. Stein, Nov 26 2016 *) CROSSREFS See A141598 for further details. Cf. also A067601, A155914, A238838. Sequence in context: A265937 A038058 A062531 * A047677 A030276 A081476 Adjacent sequences:  A141596 A141597 A141598 * A141600 A141601 A141602 KEYWORD nonn,hard,more AUTHOR Milan Gustar (artech(AT)noise.cz), Sep 03 2008 EXTENSIONS Edited by N. J. A. Sloane, Mar 15 2014 a(9) from David V. Feldman, Apr 09 2018 Definition corrected by Zack Baker, Jul 04 2018 STATUS approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)