|
|
COMMENTS
|
Also the number of "good" permutations on 2n+1 elements [Novakovich]. - N. J. A. Sloane, Feb 22 2011.
Also the number of transversals of a cyclic latin square of order 2n+1 and the number of orthomorphisms of the cyclic group of order 2n+1. - Ian M. Wanless (wanless(AT)maths.ox.ac.uk), Oct 07 2001
Also the number of complete mappings of a cyclic group of order 2n+1; also (2n+1) times the number of "standard" complete mappings of cyclic group of order 2n+1. - Jieh Hsiang, D.Frank Hsu and Yuh Pyng Shieh (arping(AT)turing.csie.ntu.edu.tw), May 08 2002
See A003111 for further information.
|
|
|
REFERENCES
|
N. J. Cavenagh and I. M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Disc. Appl. Math. 158 (2010), 136-146.
B. D. McKay, J. C. McLeod and I. M. Wanless, The number of transversals in a Latin square, Des. Codes Cryptogr., 40, (2006) 269-284.
D. Novakovic, (2000) Computation of the number of complete mappings for permutations. Cybernetics & System Analysis, No. 2, v. 36, pp. 244-247.
Yuh Pyng Shieh, Jieh Hsiang and D. Frank Hsu, On the enumeration of Abelian k-complete mappings, vol. 144 of Congressus Numerantium, 2000, pp. 67-88
Yuh Pyng Shieh, Partition Strategies for #P-complete problem with applications to enumerative combinatorics, PhD thesis, National Taiwan University, 2001
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. S. Stones and I. M. Wanless, Compound orthomorphisms of the cyclic group, Finite Fields Appl. 16 (2010), 277-289.
I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 118.
|
|
|
FORMULA
|
Suppose n is odd and let b(n)=a((n-1)/2). Then b(n) is odd; if n>3 and n is not 1 mod 3 then b(n) is divisible by 3n; b(n)=-2n mod n^2 in n is prime; b(n) is divisible by n^2 if n is composite; b(n) is asymptotically in between 3.2^n and 0.62^n n!. [Cavenagh, Wanless], [McKay, McLeod, Wanless], [Stones, Wanless] - From Ian Wanless, Jul 30 2010
|
