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Search: id:A062165
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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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+0
2
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| 1, 0, 0, 1, 1, 1, 3, 4, 13, 36, 115, 813, 3083, 21001, 131859, 868613
(list; graph; listen)
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OFFSET
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1,7
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LINKS
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M. Engelhardt, The N queens problem
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CROSSREFS
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Sequence in context: A111954 A036672 A084315 this_sequence A001056 A122151 A082732
Adjacent sequences: A062162 A062163 A062164 this_sequence A062166 A062167 A062168
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KEYWORD
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nonn,nice,more
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AUTHOR
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Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de)
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EXTENSIONS
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In this sequence, 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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