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

1, 2, 4, 24, 288, 3856, 89328, 2755968, 103653120

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

Table of n, a(n) for n=1..9.

Zackary Baker, Properties and Calculations of Constructive Orderings of Z/nZ, Minnesota J. of Undergrad. Math. (2018-2019) Vol. 4, No. 1, see p. 9.

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