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A101454
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Number of inequivalent solutions to toroidal (8n+1)-queen problem under the symmetry operator R45(x,y)=( (x-y)/sqrt(2), (x+y)/sqrt(2) ), divided by 2^n.
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0
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1, 0, 1, 0, 0, 6, 28, 0, 0, 911, 0, 16435, 107713
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OFFSET
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0,6
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COMMENTS
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The R45 operator is not valid on toroidal N-queen 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 N-queen problem has no fixed points under R45 if N is not equal to 8k+1 for some integer k.
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REFERENCES
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Jieh Hsiang, Yuh-Pyng Shieh and YaoChiang Chen, "The Cyclic Complete Mappings Counting Problems", PaPS: Problems and Problem Sets for ATP Workshop in conjunction with CADE-18 and FLoC 2002, Copenhagen, Denmark, 2002/07/27-08/01.
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LINKS
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EXAMPLE
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a(5)=6 because the number of inequivalent solutions to toroidal 41-queen problem under R45 is 192 and 192 / (2^5) = 6.
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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Yuh-Pyng Shieh, Yung-Luen Lan, Jieh Hsiang (arping(AT)turing.csie.ntu.edu.tw), Jan 19 2005
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STATUS
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approved
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