%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)=( (xy)/sqrt(2), (x+y)/sqrt(2) ), divided by 2^n.
%C 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.
%D 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.
%H YuhPyng 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 41queen problem under R45 is 192 and 192 / (2^5) = 6.
%Y Cf. A007705, A057126.
%K hard,nonn
%O 0,6
%A YuhPyng Shieh, YungLuen Lan, Jieh Hsiang (arping(AT)turing.csie.ntu.edu.tw), Jan 19 2005
