A062165 Number of ways of placing n nonattacking (normal) queens on n X n board, solutions similar on the torus count only once.

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

Offset

1,7

Comments

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).

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.

Links

Table of n, a(n) for n=1..16.

M. Engelhardt, The N queens problem

Crossrefs

Sequence in context: A286917 A084315 A194649 * A243764 A201821 A001056

Adjacent sequences: A062162 A062163 A062164 * A062166 A062167 A062168

Keyword

nonn,nice,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