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

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

Offset: 1

Author

Milan Gustar (artech(AT)noise.cz), Sep 03 2008

Keywords

• nonn
• hard
• more

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

• 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

Crossrefs

See A141598 for further details. Cf. also A067601, A155914, A238838.

Programs

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 *)

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