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Search: id:A062164
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| A062164 |
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Number of ways of placing n nonattacking (normal) queens on n X n board, solutions congruent on the torus count only once. |
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3
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| 1, 0, 0, 1, 1, 1, 3, 6, 20, 40, 191, 953, 4604, 24660, 158466, 1009395
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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In this sequence two n-queens solutions p and q are considered equivalent iff there are natural numbers 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, besides rotations and reflections, also torus shifts are allowed. The sequence reduces the objects of A002562 and via that of A000170. The reduction of A000170 to this sequence is exactly the same as from A007705 to A053994 for torus queens; however, a solution for torus queens remains always a solution after a shift while a normal queens solutions does so only sometimes.
Note that the equivalence classes of this sequence are a subset of A006841. Moreover they are a subset of A062167.
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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: A024607 A058818 A081181 this_sequence A052408 A005558 A138350
Adjacent sequences: A062161 A062162 A062163 this_sequence A062165 A062166 A062167
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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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