A062168 Number of permutations with at most 2 queens on any torus diagonal, solutions similar on the torus count only once.

1, 0, 0, 1, 2, 3, 3, 19, 31, 328, 650, 14542, 37449, 771570

Offset: 1

Author

Matthias Engelhardt

Keywords

• nonn
• more

Comments

As A062167, also this sequence counts classes of "near n-queens solutions". In this sequence, two permutations 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 if 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). The sequence contains the objects of A062165.

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