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 A000170 Number of ways of placing n nonattacking queens on an n X n board. (Formerly M1958 N0775) 84
 1, 1, 0, 0, 2, 10, 4, 40, 92, 352, 724, 2680, 14200, 73712, 365596, 2279184, 14772512, 95815104, 666090624, 4968057848, 39029188884, 314666222712, 2691008701644, 24233937684440, 227514171973736, 2207893435808352, 22317699616364044, 234907967154122528 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For n > 3, a(n) is the number of maximum independent vertex sets in the n X n queen graph. - Eric W. Weisstein, Jun 20 2017 Number of nodes on level n of the backtrack tree for the n queens problem (a(n) = A319284(n, n)). - Peter Luschny, Sep 18 2018 Number of permutations of [1...n] such that |p(j)-p(i)| != j-i for i infinity} (1/n) * log(n!/a(n)) = constant = 0.90.... - Benoit Cloitre, Nov 10 2002 Lim_{n->infinity} a(n)^(1/n)/n = exp(-A359441) = 0.1431301... [Simkin 2021]. - Vaclav Kotesovec, Jan 01 2023 EXAMPLE a(2) = a(3) = 0, since on 2 X 2 and 3 X 3 chessboards there are no solutions. . a(4) = 2: +---------+ +---------+ | . . Q . | | . Q . . | | Q . . . | | . . . Q | | . . . Q | | Q . . . | | . Q . . | | . . Q . | +---------+ +---------+ a(5) = 10: +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ | . . . Q . | | . . Q . . | | . . . . Q | | . . . Q . | | . . . . Q | | . Q . . . | | . . . . Q | | . . Q . . | | Q . . . . | | . Q . . . | | . . . . Q | | . Q . . . | | Q . . . . | | . . Q . . | | . . . Q . | | . . Q . . | | . . . Q . | | . . . Q . | | . . . . Q | | Q . . . . | | Q . . . . | | Q . . . . | | . Q . . . | | . Q . . . | | . . Q . . | +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ | Q . . . . | | . Q . . . | | Q . . . . | | . . Q . . | | . Q . . . | | . . . Q . | | . . . . Q | | . . Q . . | | Q . . . . | | . . . Q . | | . Q . . . | | . . Q . . | | . . . . Q | | . . . Q . | | Q . . . . | | . . . . Q | | Q . . . . | | . Q . . . | | . Q . . . | | . . Q . . | | . . Q . . | | . . . Q . | | . . . Q . | | . . . . Q | | . . . . Q | +-----------+ +-----------+ +-----------+ +-----------+ +-----------+ a(6) = 4: +-------------+ +-------------+ +-------------+ +-------------+ | . . . . Q . | | . . . Q . . | | . . Q . . . | | . Q . . . . | | . . Q . . . | | Q . . . . . | | . . . . . Q | | . . . Q . . | | Q . . . . . | | . . . . Q . | | . Q . . . . | | . . . . . Q | | . . . . . Q | | . Q . . . . | | . . . . Q . | | Q . . . . . | | . . . Q . . | | . . . . . Q | | Q . . . . . | | . . Q . . . | | . Q . . . . | | . . Q . . . | | . . . Q . . | | . . . . Q . | +-------------+ +-------------+ +-------------+ +-------------+ - Hugo Pfoertner, Mar 17 2019 CROSSREFS See A140393 for another version. Cf. A002562, A065256. Cf. A036464 (2Q), A047659 (3Q), A061994 (4Q), A108792 (5Q), A176186 (6Q). Cf. A099152, A006717, A051906, A319284 (backtrack trees). Main diagonal of A348129. Sequence in context: A189869 A054790 A140393 * A038216 A213603 A145911 Adjacent sequences: A000167 A000168 A000169 * A000171 A000172 A000173 KEYWORD nonn,hard,nice AUTHOR N. J. A. Sloane EXTENSIONS 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). a(24) from Kenji KISE (kis(AT)is.uec.ac.jp), Sep 01 2004 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. 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. 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, Jun 18 2008 It now appears that this sequence (A000170) is correct and A140393 is wrong. - N. J. A. Sloane, Nov 08 2008 Added a(26) as calculated by Queens(AT)TUD [http://queens.inf.tu-dresden.de/]. - Thomas B. Preußer, Jul 11 2009 Added a(27) as calculated by the Q27 Project [https://github.com/preusser/q27]. - Thomas B. Preußer, Sep 23 2016 a(0) = 1 prepended by Joerg Arndt, Sep 16 2018 STATUS approved

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Last modified June 23 17:30 EDT 2024. Contains 373653 sequences. (Running on oeis4.)