A062165 - OEIS

%I #7 Mar 30 2012 18:59:35

%S 1,0,0,1,1,1,3,4,13,36,115,813,3083,21001,131859,868613

%N Number of ways of placing n nonattacking (normal) queens on n X n board, solutions similar on the torus count only once.

%C Two n-queens solutions p and q are considered similar iff there is a factor f, 0 < f < n, satisfying gcd (f,n) = 1, such that for all k from {0, ..., n-1} q (k * f mod n) = p (k) * f mod n or q is a rotation, a reflection or a shift of such a q. In other words, also expansions are allowed which move the queen at (k, p(k)) to (f * k mod n, f * p(k) mod n).

%C The sequence reduces exactly the objects of A062164 and, via that sequence, these of A002562 and A000170. Note that the equivalence classes of this sequence are a subset of A062168.

%H M. Engelhardt, <a href="http://www.nqueens.de">The N queens problem</a>

%K nonn,nice,more

%O 1,7

%A _Matthias Engelhardt_

%E Updated link that is transferred from people.freenet.de/nQueens to www.nqueens.de _Matthias Engelhardt_, Apr 21 2010