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Search: id:A062167
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| A062167 |
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Number of permutations with at most 2 queens on any torus diagonal, solutions congruent on the torus count only once. |
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+0
3
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| 1, 0, 0, 1, 2, 3, 5, 29, 93, 569, 3226, 28630, 221250, 2314650
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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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.
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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: A038962 A019400 A084599 this_sequence A107451 A093490 A073309
Adjacent sequences: A062164 A062165 A062166 this_sequence A062168 A062169 A062170
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KEYWORD
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nonn,more
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AUTHOR
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Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de)
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