A006841 Permutation arrays of period n. (Formerly M1225)

1, 1, 1, 2, 4, 10, 28, 127, 686, 4975, 42529, 420948, 4622509, 55670332, 726738971, 10217376792, 153848448652, 2470073249960, 42120966152815, 760282326662191, 14481561464994821, 290289454462745374, 6108699653117045614

Offset

1,4

Comments

Also superpositions of cycles of order n of the groups S_2 and D_n. - Sean A. Irvine, Oct 25 2017

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 171.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. P. Street and R. Day, Sequential binary arrays II: Further results on the square grid, pp. 392-418 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.

Links

Table of n, a(n) for n=1..23.

M. Engelhardt, Java program

V. Meally, Letter to N. J. A. Sloane, Feb 1975

E. M. Palmer and R. W. Robinson, Enumeration under two representations of the wreath product, Acta Math., 131 (1973), 123-143. (See Table 2, but note errors.)

A. P. Street and R. Day, Sequential binary arrays II: Further results on the square grid, pp. 392-418 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982. (Annotated scanned copy)

Venta Terauds, J. Sumner, Circular genome rearrangement models: applying representation theory to evolutionary distance calculations, arXiv preprint arXiv:1712.00858 [q-bio.PE], 2017.

Formula

Asymptotic behavior: The n-th term T(n) is always larger than n! / (8*n^2) = (n-1)! / 8n; for large n, it is approximated by that value. Stated as formula: T(n) > (n-1)! / 8n; lim 8n * T(n) / (n-1) = 1 as n tends to infinity.

Crossrefs

Cf. A061417.

Sequence in context: A352068 A123429 A207018 * A003223 A061417 A153921

Adjacent sequences: A006838 A006839 A006840 * A006842 A006843 A006844

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Terms for n=1..8 from A. P. Street and R. Day; other terms computed by Matthias Engelhardt. For n=9..12, he used a program which shifts, rotates and mirrors permutations. Terms for n=13..29 computed with a Java program implementing the formulas.

Status

approved