cp's OEIS Frontend

A141599 Number of difference sets for permutations of [2n] with distinct differences.

%I A141599 #54 Nov 02 2021 12:21:44
%S A141599 1,2,4,24,288,3856,89328,2755968,103653120
%N A141599 Number of difference sets for permutations of [2n] with distinct differences.
%C A141599 Number of all-interval rows for systems with 2n notes in the octave (2n-edo).
%C A141599 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
%C A141599 No permutations of the integers from 0 to 2n can generate such a complete sequence. - _Ian Duff_, Dec 25 2018
%H A141599 Zackary Baker, <a href="https://pubs.lib.umn.edu/index.php/mjum/article/view/4154">Properties and Calculations of Constructive Orderings of Z/nZ</a>, Minnesota J. of Undergrad. Math. (2018-2019) Vol. 4, No. 1, see p. 9.
%H A141599 E. N. Gilbert, <a href="http://www.jstor.org/stable/2027267">Latin squares which contain no repeated digrams</a>, SIAM Rev. 7 1965 189--198. MR0179095 (31 #3346). Mentions this sequence. - _N. J. A. Sloane_, Mar 15 2014
%H A141599 Milan Gustar, <a href="http://www.uvnitr.cz/music_theory/rady.html">More information</a>
%H A141599 Milan Gustar, <a href="http://www.uvnitr.cz/downloads.html">Programs and data</a>
%t A141599 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 *)
%Y A141599 See A141598 for further details. Cf. also A067601, A155914, A238838.
%K A141599 nonn,hard,more
%O A141599 1,2
%A A141599 Milan Gustar (artech(AT)noise.cz), Sep 03 2008
%E A141599 Edited by _N. J. A. Sloane_, Mar 15 2014
%E A141599 a(9) from _David V. Feldman_, Apr 09 2018
%E A141599 Definition corrected by _Zack Baker_, Jul 04 2018