A062166 Number of ways of placing n nonattacking torus queens on 2n+1 X 2n+1 board, similar solutions count only once.

1, 0, 1, 1, 0, 2, 7, 0, 26, 46, 0, 2861, 40303, 0, 6446047

Offset

1,6

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 A053994 and, via that sequence, these of A007705.

Links

Table of n, a(n) for n=1..15.

M. Engelhardt, The N queens problem

Crossrefs

Sequence in context: A282072 A282493 A355348 * A281673 A281847 A282206

Adjacent sequences: A062163 A062164 A062165 * A062167 A062168 A062169

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