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A071607 Number of strong complete mappings of the cyclic group Z_{2n+1}. 2
1, 0, 2, 4, 0, 8, 348, 0, 8276, 43184, 0, 5602176, 78309000, 0, 20893691564 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A strong complete mapping of a cyclic group (Zn,+) is a permutation f(x) of Zn such that f(0)=0 and that f(x)-x and f(x)+x are both permutations.

a(n)=TQ(n)/n where TQ(n) is the number of solutions of toroidal n-queen problem (A007705).

REFERENCES

Anthony B. Evans,"Orthomorphism Graphs of Groups", vol. 1535 of Lecture Notes in Mathematics, Springer-Verlag, 1991.

D. Novakovic, (2000) Computation of the number of complete mappings for permutations. Cybernetics & System Analysis, No. 2, v. 36, pp. 244-247.

I. Rivin, I. Vardi and P. Zimmermann, "The n-queens problem", vol. 101 of Amer. Math. Monthly, 1994, pp. 629-639.

Y. P. Shieh, J. Hsiang and D. F. Hsu, "On the enumeration of Abelian k-complete mappings", vol. 144 of Congressus Numerantium, 2000, pp. 67-88.

LINKS

Table of n, a(n) for n=0..14.

Y. P. Shieh, Cyclic complete mappings counting problems

EXAMPLE

f(x)=2x in (Z7,+) is a strong complete mapping of Z7 since f(0)=0 and both f(x)-x (=x) and f(x)+x (=3x) are permutations of Z7.

CROSSREFS

Sequence in context: A115341 A101160 A103191 * A095059 A021419 A180192

Adjacent sequences:  A071604 A071605 A071606 * A071608 A071609 A071610

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified December 20 10:32 EST 2014. Contains 252241 sequences.