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Search: id:A101453
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| A101453 |
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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) ). |
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+0
1
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| 1, 0, 4, 0, 0, 192, 1792, 0, 0, 466432, 0, 33658880, 441192448
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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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Yuh-Pyng Shieh, Complete Mappings
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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.
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CROSSREFS
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Cf. A007705, A057126.
Sequence in context: A071608 A013451 A013462 this_sequence A128131 A115713 A115633
Adjacent sequences: A101450 A101451 A101452 this_sequence A101454 A101455 A101456
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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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