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A099152
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Number of n X n permutation matrices in which the sums of the entries of each NorthEast-SouthWest diagonal are 0 or 1.
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15
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1, 1, 3, 7, 23, 83, 405, 2113, 12657, 82297, 596483, 4698655, 40071743, 367854835, 3622508685, 38027715185, 424060091065, 5006620130753, 62395131973755, 818456924866815
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Numbers of solutions to a modified version of the n-queens problem, in which two queens do not attack each other if they are in the same NorthWest-SouthEst diagonal.
Number of perfect extremal Skolem-type sequences of order n.
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 28 2008: (Start)
a(n) is also the number of permutations p of {1,2,...,n} for which the numbers p(i)-i (i=1,2,...,n) are distinct. Example: a(4)=7 because we have 4132, 3142, 2413, 4213, 2431, 3241 and 4321.
a(n) is also the number of permutations p of {1,2,...,n} for which the numbers p(i)+i (i=1,2,...,n) are distinct. Example: a(4)=7 because we have 1423, 2413, 3142, 1342, 3124, 2314 and 1234.
a(n)=A125182(n,n). (End)
Also number of transversals in the n X n matrix M defined by M_{ij} = i+j. [Cavenagh-Wanless]
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REFERENCES
| N. J. Cavenagh and I. M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Disc. Appl. Math. 158 (2010), 136-146.
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LINKS
| G. Nordh, Perfect Skolem sequences
W. Schubert, N-Queens page
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CROSSREFS
| A125182 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 28 2008]
Sequence in context: A169650 A136508 A184935 * A113860 A080355 A100964
Adjacent sequences: A099149 A099150 A099151 * A099153 A099154 A099155
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KEYWORD
| nonn,more
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AUTHOR
| Cecilia Bebeacua and Simone Severini (simoseve(AT)gmail.com), Nov 16 2004
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EXTENSIONS
| More terms from Ivica Kolar (telpro(AT)kvid.hr), Nov 23 2004
a(14)-a(18) from Ian Wanless, Jul 30 2010, from the Cavenagh-Wanless paper.
a(19),a(20) from W. Schubert (wschubnq(AT)gmx.de), May 27 2011
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