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

1,5

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

Table of n, a(n) for n=1..14.

M. Engelhardt, The N queens problem

Crossrefs

Sequence in context: A090522 A114728 A057676 * A296836 A019229 A135353

Adjacent sequences: A062165 A062166 A062167 * A062169 A062170 A062171

Keyword

nonn,more

Author

Matthias Engelhardt

Extensions

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

Status

approved