%I A101453
%S A101453 1,0,4,0,0,192,1792,0,0,466432,0,33658880,441192448
%N A101453 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) ).
%C A101453 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 A101453 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 A101453 Yuh-Pyng Shieh, <a href="http://turing.csie.ntu.edu.tw/~arping/cm">Complete 
               Mappings </a>
%e A101453 a(5)=6 because the number of inequivalent solutions to toroidal 41-queen 
               problem under R45 is 192.
%Y A101453 Cf. A007705, A057126.
%Y A101453 Sequence in context: A071608 A013451 A013462 this_sequence A128131 A115713 
               A115633
%Y A101453 Adjacent sequences: A101450 A101451 A101452 this_sequence A101454 A101455 
               A101456
%K A101453 hard,nonn
%O A101453 0,3
%A A101453 Yuh-Pyng Shieh, Yung-Luen Lan, Jieh Hsiang (arping(AT)turing.csie.ntu.edu.tw), 
               Jan 19 2005