A062167 Number of permutations with at most 2 queens on any torus diagonal, solutions congruent on the torus count only once.

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

Offset: 1

Author

Matthias Engelhardt

Keywords

• nonn
• more

Comments

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).

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.

Links

• M. Engelhardt, The N queens problem

Extensions

Updated link that is transferred from people.freenet.de/nQueens to www.nqueens.de Matthias Engelhardt, Apr 21 2010