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A101454 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. 0

%I

%S 1,0,1,0,0,6,28,0,0,911,0,16435,107713

%N 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.

%C 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.

%D 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.

%H Yuh-Pyng Shieh, <a href="http://turing.csie.ntu.edu.tw/~arping/cm">Complete Mappings</a>

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

%Y Cf. A007705, A057126.

%K hard,nonn

%O 0,6

%A Yuh-Pyng Shieh, Yung-Luen Lan, Jieh Hsiang (arping(AT)turing.csie.ntu.edu.tw), Jan 19 2005

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Last modified May 29 08:12 EDT 2022. Contains 354124 sequences. (Running on oeis4.)