Search: id:A000170
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%I A000170 M1958 N0775
%S A000170 1,0,0,2,10,4,40,92,352,724,2680,14200,73712,365596,2279184,14772512,
%T A000170 95815104,666090624,4968057848,39029188884,314666222712,2691008701644,
%U A000170 24233937684440,227514171973736,2207893435808352,22317699616364044
%N A000170 Number of ways of placing n nonattacking queens on n X n board.
%D A000170 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000170 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000170 J. R. Bitner and E. M. Reingold, Backtrack programming techniques, Commun. 
               ACM, 18 (1975), 651-656.
%D A000170 J. Freeman, A neural network solution to the n-queens problem, The Mathematica 
               J., 3 (No. 3, 1993), 52-56.
%D A000170 M. Gardner, The Unexpected Hanging, pp. 190-2, Simon & Shuster NY 1969
%D A000170 Jieh Hsiang, Yuh-Pyng Shieh and Yao-Chiang Chen, The cyclic complete 
               mappings counting problems, in Problems and Problem Sets for ATP, 
               volume 02-10 of DIKU technical reports, G. Sutcliffe, J. Pelletier 
               and C. Suttner, eds., 2002.
%D A000170 Kenji Kise, Takahiro Katagiri, Hiroki Honda and Toshitsugu Yuba: Solving 
               the 24-queens Problem using MPI on a PC Cluster, Technical Report 
               UEC-IS-2004-6, Graduate School of Information Systems, The University 
               of Electro-Communications (2004)
%D A000170 I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. 
               Monthly, 101 (1994), 629-639.
%D A000170 M. A. Sainte-Lagu\"{e}, Les R\'{e}seaux (ou Graphes), M\'{e}morial des 
               Sciences Math\'{e}matiques, Fasc. 18, Gauthier-Villars, Paris, 1926, 
               p. 47.
%D A000170 R. J. Walker, An enumerative technique for a class of combinatorial problems, 
               pp. 91-94 of Proc. Sympos. Applied Math., vol. 10, Amer. Math. Soc., 
               1960.
%D A000170 M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, 
               p. 238.
%H A000170 Amazing Mathematical Object Factory, <a href="http://theory.cs.uvic.ca/
               amof/e_queeI.htm">Information on the n Queens problem</a> [Link corrected 
               by Gerry Myerson, Apr 08 2009]
%H A000170 Anonymous, <a href="http://138.26.80.106:8080/literature.html">N Queens 
               Problem</a>
%H A000170 D. Bill, <a href="http://www.durangobill.com/N_Queens.html">Durango Bill's 
               The N-Queens Problem</a> [Broken link?]
%H A000170 Patrick GUILLEMIN, <a href="http://www.etsi.org/plugtests/GRID.htm">N-Queens 
               Challenge</a> [Broken link?]
%H A000170 Patrick GUILLEMIN, <a href="http://www.etsi.org/plugtests/Upcoming/GRID/
               GRIDcontest.htm">N-Queens Challenge</a> [Broken link?]
%H A000170 Patrick GUILLEMIN, <a href="http://www.etsi.org/plugtests/Upcoming/GRID/
               GRIDremotechallenge.htg">N-Queens Challenge</a> [Broken link?]
%H A000170 Kenji KISE, <a href="http://www.yuba.is.uec.ac.jp/~kis/doc/paper/uec-is-2004-06.pdf">
               24-queens</a>.
%H A000170 W. Kosters, <a href="http://www.liacs.nl/home/kosters/nqueens.html">n-Queens 
               (Extensive Bibliography)</a>
%H A000170 NQuens@home, <a href="http://nqueens.ing.udec.cl/">Home Page</a>
%H A000170 Objectweb ProActive INRIA Team, <a href="http://proactive.objectweb.org">
               Home Page</a>
%H A000170 Objectweb ProActive INRIA Team, <a href="http://www-sop.inria.fr/oasis/
               ProActive/apps/nqueen.html">Solve the N Queens challenge with ProActive 
               !</a>
%H A000170 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               QueensProblem.html">Link to a section of The World of Mathematics.</
               a>
%H A000170 <a href="http://queens.inf.tu-dresden.de/">Queens(AT)TUD</a> project 
               website. [From Thomas B. Preusser (thomas.preusser(AT)tu-dresden.de), 
               Jul 11 2009]
%F A000170 Strong conjecture : there is a constant c around 2.54 such that a(n) 
               is asymptotic to n!/c^n; weak conjecture : lim n -> infinity (1/n) 
               * ln(n!/a(n)) = constant =0.90.... - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Nov 10 2002
%e A000170 a(2) = a(3) = 0, since on 2 X 2 and 3 X 3 chessboards there are no solutions.
%Y A000170 See A140393 for another version. Cf. A002562, A065256.
%Y A000170 Sequence in context: A029673 A054790 A140393 this_sequence A038216 A145911 
               A027626
%Y A000170 Adjacent sequences: A000167 A000168 A000169 this_sequence A000171 A000172 
               A000173
%K A000170 nonn,hard,nice
%O A000170 1,4
%A A000170 N. J. A. Sloane (njas(AT)research.att.com).
%E A000170 Terms for n=21-23 computed by Sylvain PION (Sylvain.Pion(AT)sophia.inria.fr) 
               and Joel-Yann FOURRE (Joel-Yann.Fourre(AT)ens.fr).
%E A000170 a(24) from Kenji KISE (kis(AT)is.uec.ac.jp), Sep 01 2004
%E A000170 a(25) from Objectweb ProActive INRIA Team (proactive(AT)objectweb.org), 
               Jun 11 2005 [Communicated by Alexandre Di Costanzo (Alexandre.Di_Costanzo(AT)sophia.inria.fr)]. 
               This calculation took about 53 years of CPU time.
%E A000170 a(25) has been confirmed by the NTU 25Queen Project at National Taiwan 
               University and Ming Chuan University, led by Yuh-Pyng (Arping) Shieh, 
               Jul 26 2005. This computation took 26613 days CPU time.
%E A000170 Some of the links may be broken. I would appreciate receiving updates 
               to them. - N. J. A. Sloane (njas(AT)research.att.com), May 01 2006
%E A000170 The NQueens-at-Home web site gives a different value for a(24), 226732487925864. 
               Thanks to Goran Fagerstrom for pointing this out. I do not know which 
               value is correct. I have therefore created a new entry, A140393, 
               which gives the NQueens-at-home version of the sequence. - N. J. 
               A. Sloane (njas(AT)research.att.com), Jun 18 2008
%E A000170 It now appears that this sequence (A000170) is correct and A140393 is 
               wrong. - N. J. A. Sloane (njas(AT)research.att.com), Nov 08 2008
%E A000170 Added a(26) as calculated by Queens(AT)TUD [http://queens.inf.tu-dresden.de/
               ]. Thomas B. Preusser (thomas.preusser(AT)tu-dresden.de), Jul 11 
               2009

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