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A006841 Permutation arrays of period n.
(Formerly M1225)
10

%I M1225

%S 1,1,1,2,4,10,28,127,686,4975,42529,420948,4622509,55670332,726738971,

%T 10217376792,153848448652,2470073249960,42120966152815,

%U 760282326662191,14481561464994821,290289454462745374,6108699653117045614

%N Permutation arrays of period n.

%C Also superpositions of cycles of order n of the groups S_2 and D_n. - _Sean A. Irvine_, Oct 25 2017

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

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

%D 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.

%H M. Engelhardt, <a href="/A006841/a006841.txt">Java program</a>

%H V. Meally, <a href="/A003223/a003223.pdf">Letter to N. J. A. Sloane, Feb 1975</a>

%H E. M. Palmer and R. W. Robinson, <a href="http://dx.doi.org/10.1007/BF02392038">Enumeration under two representations of the wreath product</a>, Acta Math., 131 (1973), 123-143. (See Table 2, but note errors.)

%H A. P. Street and R. Day, <a href="/A006841/a006841.pdf">Sequential binary arrays II: Further results on the square grid</a>, 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)

%H Venta Terauds, J. Sumner, <a href="https://arxiv.org/abs/1712.00858">Circular genome rearrangement models: applying representation theory to evolutionary distance calculations</a>, arXiv preprint arXiv:1712.00858 [q-bio.PE], 2017.

%F 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.

%Y Cf. A061417.

%K nonn,nice

%O 1,4

%A _N. J. A. Sloane_

%E 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.

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Last modified January 17 09:54 EST 2020. Contains 330949 sequences. (Running on oeis4.)