Search: id:A140450
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%I A140450
%S A140450 1,6,18,26,15,171,42,876,333,975,517,3066,1365,26495,20280,160712,91222,
%T A140450 743229,48184,3992510,179592,38217905,584591,9878316,1216775,10339849,
%U A140450 12263400,84175966,44434525,1692888135,408773285,2799725104,4618568460
%N A140450 The count of how many queens must be placed tentatively onto a board 
               while seeking a first solution to the "N-Queens on an N x N chessboard" 
               puzzle. The term a(4) with the value 26 is the count for a board 
               size of 4 squares by 4 squares. The highest term so far a(45) is 
               the count for a board of 45 squares by 45 squares.
%C A140450 This whole sequence refers only to the number of queen pieces placed
%C A140450 tentatively on a board in the hunt for the FIRST POSSIBLE solution for 
               each board size. This sequence makes no reference to queen placements 
               needed to hunt for subsequent solutions that are possible for board 
               sizes above 3x3.
%D A140450 CSP Queens - Counting Queen-placements http://queens.cspea.co.uk/
%D A140450 Eight Queens Puzzle, http://en.wikipedia.org/wiki/Eight_queens_puzzle
%H A140450 Colin S. Pearson, <a href="b140450.txt">Table of n, a(n) for n = 1..45</
               a> [Corrected Jul 31 2008]
%H A140450 Colin S. Pearson, <a href="http://queens.cspea.co.uk/">CSP Queens - Counting 
               Queen-placements</a>
%H A140450 Martin S. Pearson, <a href="http://queens.lyndenlea.info/">Queens On 
               A Chessboard</a>
%e A140450 Using a simple, mechanical and naive "one queen at a time" algorithm 
               (in other words, a computer-friendly algorithm), in order to place 
               4 non-clashing queens on a simple board of 4 x 4 squares, we will 
               need to place a tentative new queen 26 times before we discover the 
               first combination that allows all queens to sit unchallenged. For 
               a board size of 5 x 5 we will need to place tentative new queens 
               just 15 times before we discover the first combination of 5 unchallenged 
               queens. In this extended and corrected sequence, those figures "26" 
               and "15" are the values of terms a(4) and a(5) above.
%o A140450 A step-by-step example of this algorithm applied to 5 Queens on a 5 X 
               5 board is displayed on the web site at http://queens.cspea.co.uk/
               . In addition, a free Microsoft Windows WIN32s-based program can 
               be downloaded from the same website. The program generates and displays 
               these terms for any board size up to 32 squares by 32 squares.
%Y A140450 Cf. A000170 = Number of ways of placing n nonattacking queens on n X 
               n board; A002562 = Number of ways of placing n nonattacking queens 
               on n X n board (symmetric solutions count only once); A141843 = Triangular 
               array of lexicographically first solutions to the n queens problem.
%Y A140450 Sequence in context: A028887 A051395 A028558 this_sequence A157800 A077660 
               A030568
%Y A140450 Adjacent sequences: A140447 A140448 A140449 this_sequence A140451 A140452 
               A140453
%K A140450 nonn
%O A140450 1,2
%A A140450 Colin S. Pearson and Martin S. Pearson, Jun 26 2008, Jun 30 2008, Jul 
               03 2008, Jul 31 2008, Aug 16 2008
%E A140450 Edited by Colin S Pearson to update the URL for Martin S Pearson's website 
               Colin S Pearson (awayon(AT)cspea.co.uk), Mar 25 2009

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