

A071706


Number of complete mappings f(x) of the cyclic group Z_{2n+1} such that f(x)=f.


2



1, 1, 3, 5, 21, 69, 319, 1957, 12513, 85445, 656771, 5591277, 51531405, 509874417, 5438826975, 62000480093, 752464463029, 9685138399785, 131777883431119
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OFFSET

1,3


COMMENTS

A complete mapping of a cyclic group (Zn,+) is a permutation f(x) of Zn such that f(0)=0 and that f(x)x is also a permutation.
a(n) is the number of complete mappings fixed under rotation R180 where R180(f)(x)=f(x). This sequence (n) equals TSQ_R180(n), the number of solutions of the toroidal nqueen problem fixed under rotation R180. A solution of toroidalsemi nqueen problem is a permutation f(x) of Zn such that f(x)x is also a permutation.


REFERENCES

Y. P. Shieh, "Partition strategies for #Pcomplete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
Y. P. Shieh, J. Hsiang and D. F. Hsu, "On the enumeration of Abelian kcomplete mappings", vol. 144 of Congressus Numerantium, 2000, pp. 6788.


LINKS

Table of n, a(n) for n=1..19.
Y. P. Shieh, Cyclic complete mappings counting problems


EXAMPLE

f(x)=6x in (Z7,+) is a complete mapping of Z7 since that f(0)=0 and that f(x)x (=5x) is also a permutation of Z7. R180(f)(x)=f(x) (=6x). So f(x) is fixed under R180.


CROSSREFS

Sequence in context: A264683 A286033 A056803 * A196418 A189560 A216385
Adjacent sequences: A071703 A071704 A071705 * A071707 A071708 A071709


KEYWORD

nonn


AUTHOR

J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002


STATUS

approved



