cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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

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

A067601 a(n) is the number of inequivalent permutations of {0..2n-1}, such that the first differences (modulo 2n) are a permutation of {1..2n-1}.

Original entry on oeis.org

1, 1, 2, 12, 144, 1928, 44664, 1377984, 51826560
Offset: 1

Views

Author

Eugene McDonnell (eemcd(AT)aol.com), Jan 31 2002

Keywords

Comments

"Inequivalent" effectively means that the permutation begins with 0 and the second item is <= n. (Working modulo 2n, s1+k,s2+k,s3+k,... is equivalent to s1,s2,s3,...; and -s1,-s2,-s3 is equivalent to s1,s2,s3,...)
The references all deal with length 12.

Examples

			0 1 3 2 has first difference, mod 4, of 1 2 3;
0 2 1 4 5 3 has first difference, mod 6, of 2 5 3 1 4;
0 4 5 8 3 1 7 9 2 11 10 6 has first difference, mod 12, of 4 1 3 7 10 6 2 5 9 11 8.
		

Crossrefs

Formula

a(n) = ceiling(A141599(n)/2). - Leo C. Stein, Nov 26 2016

Extensions

Edited by Don Reble, Oct 31 2005
a(9) from Sean A. Irvine, Dec 22 2023

A155914 Example of an all interval series: the 12 integers 0..11 sorted such that the first differences contain all numbers from 1 to 11 (mod 12).

Original entry on oeis.org

0, 11, 7, 4, 2, 9, 3, 8, 10, 1, 5, 6
Offset: 1

Views

Author

Craig Bourne (cbourne(AT)cbourne.com), Jan 30 2009

Keywords

Comments

"All-interval" means that the differences 11-0=11, 7-11=-4, 4-7=-3, ..., 6-5=1 read modulo 12 contain all numbers (intervals) from 1 to 11.
This is one of 3856 such sequences.
The Anders link contains a source program written in Strasheela, formulated as a constrained satisfaction problem (CSP).

References

  • Robert Morris and Daniel Starr, The Structure of All-Interval Series, 1974, Yale University Department of Music.

Crossrefs

A307852 Number of equivalence classes of rotational row complete Latin squares of order 2n under Gilbert transformations.

Original entry on oeis.org

1, 1, 2, 22, 267
Offset: 1

Views

Author

Beth Malmskog, May 01 2019

Keywords

Crossrefs

A141598 is the number of rotational row complete Latin squares of order 2n; the current sequence is the number of equivalence classes of items counted in A141598.

Programs

  • Python
    # See Malmskog link.
Showing 1-4 of 4 results.