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Number of permutations with at most 2 queens on any torus diagonal, solutions congruent on the torus count only once.
2

%I #6 Mar 30 2012 18:59:35

%S 1,0,0,1,2,3,5,29,93,569,3226,28630,221250,2314650

%N Number of permutations with at most 2 queens on any torus diagonal, solutions congruent on the torus count only once.

%C This sequence counts classes of "near n-queens solutions". Permutations with at most 1 queen on any torus diagonal are exactly the torus n queen solutions (A007705), those with at most 2 contain the normal n queen solutions (A000170).

%C Therefore they may be called "near n-queens solutions". In this sequence, permutations p and q are considered equivalent iff there are natural 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. In other words, rotations, reflections and torus shifts are allowed. The sequence contains the objects of A062164.

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

%K nonn,more

%O 1,5

%A _Matthias Engelhardt_

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