

A101453


Number of inequivalent solutions to toroidal (8n+1)queen problem under the symmetry operator R45(x,y)=( (xy)/sqrt(2), (x+y)/sqrt(2) ).


0



1, 0, 4, 0, 0, 192, 1792, 0, 0, 466432, 0, 33658880, 441192448
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OFFSET

0,3


COMMENTS

The R45 operator is not valid on toroidal Nqueen problem if 2 is not a perfect square modulo N. For example, a(3)=0 is because 2 is not a perfect square modulo 25. see A057126. Toroidal Nqueen problem has no fixed points under R45 if N is not equal to 8k+1 for some integer k.


REFERENCES

Jieh Hsiang, YuhPyng Shieh and YaoChiang Chen, "The Cyclic Complete Mappings Counting Problems", PaPS: Problems and Problem Sets for ATP Workshop in conjunction with CADE18 and FLoC 2002, Copenhagen, Denmark, 2002/07/2708/01.


LINKS

Table of n, a(n) for n=0..12.
YuhPyng Shieh, Complete Mappings


EXAMPLE

a(5)=6 because the number of inequivalent solutions to toroidal 41queen problem under R45 is 192.


CROSSREFS

Cf. A007705, A057126.
Sequence in context: A013462 A326862 A222325 * A222399 A222519 A128131
Adjacent sequences: A101450 A101451 A101452 * A101454 A101455 A101456


KEYWORD

hard,nonn


AUTHOR

YuhPyng Shieh, YungLuen Lan, Jieh Hsiang (arping(AT)turing.csie.ntu.edu.tw), Jan 19 2005


STATUS

approved



