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
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
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