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A062165
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Number of ways of placing n nonattacking (normal) queens on n X n board, solutions similar on the torus count only once.
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1
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1, 0, 0, 1, 1, 1, 3, 4, 13, 36, 115, 813, 3083, 21001, 131859, 868613
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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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.
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LINKS
| M. Engelhardt, The N queens problem
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CROSSREFS
| Sequence in context: A174684 A084315 A194649 * A201821 A001056 A122151
Adjacent sequences: A062162 A062163 A062164 * A062166 A062167 A062168
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KEYWORD
| nonn,nice,more,changed
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AUTHOR
| Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de)
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EXTENSIONS
| Updated link that is transferred from people.freenet.de/nQueens to www.nqueens.de Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de), Apr 21 2010
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