

A141599


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


6




OFFSET

1,2


COMMENTS

Number of allinterval rows for systems with 2n notes in the octave (2nedo).
As determined by direct enumeration up to n=6, a(n) is the number of circular permutations of the integers from 0 to 2n1 in which all "steppingon" 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. (20182019) Vol. 4, No. 1, see p. 9.
E. N. Gilbert, Latin squares which contain no repeated digrams, SIAM Rev. 7 1965 189198. 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



