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

1,5

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

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

M. Engelhardt, The N queens problem

Crossrefs

Sequence in context: A354084 A331399 A084599 * A358896 A279189 A107451

Adjacent sequences: A062164 A062165 A062166 * A062168 A062169 A062170

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