%I A062164
%S A062164 1,0,0,1,1,1,3,6,20,40,191,953,4604,24660,158466,1009395
%N A062164 Number of ways of placing n nonattacking (normal) queens on n X n board, 
               solutions congruent on the torus count only once.
%C A062164 In this sequence two n-queens solutions p and q are considered equivalent 
               iff there are natural numbers x and y such that, for all k from {0, 
               ..., n-1}, q (k + x mod n) = p (k) + y mod n, or q is a rotation 
               or a reflection of such a q.
%C A062164 In other words, besides rotations and reflections, also torus shifts 
               are allowed. The sequence reduces the objects of A002562 and via 
               that of A000170. The reduction of A000170 to this sequence is exactly 
               the same as from A007705 to A053994 for torus queens; however, a 
               solution for torus queens remains always a solution after a shift 
               while a normal queens solutions does so only sometimes.
%C A062164 Note that the equivalence classes of this sequence are a subset of A006841. 
               Moreover they are a subset of A062167.
%H A062164 M. Engelhardt, <a href="http://people.freenet.de/nQueens">The N queens 
               problem</a>
%Y A062164 Sequence in context: A024607 A058818 A081181 this_sequence A052408 A148573 
               A148574
%Y A062164 Adjacent sequences: A062161 A062162 A062163 this_sequence A062165 A062166 
               A062167
%K A062164 nonn,nice,more
%O A062164 1,7
%A A062164 Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de)