

A101454


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


0



1, 0, 1, 0, 0, 6, 28, 0, 0, 911, 0, 16435, 107713
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OFFSET

0,6


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



EXAMPLE

a(5)=6 because the number of inequivalent solutions to toroidal 41queen problem under R45 is 192 and 192 / (2^5) = 6.


CROSSREFS



KEYWORD

hard,nonn


AUTHOR

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


STATUS

approved



