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A141843 Triangular array T(n,k) (n >= 1, 1 <= k <= n) read by rows: row n gives the lexicographically earliest solution to the n queens problem, or n zeros if no solution exists. The k-th queen is placed in square (k, T(n, k)). 5

%I

%S 1,0,0,0,0,0,2,4,1,3,1,3,5,2,4,2,4,6,1,3,5,1,3,5,7,2,4,6,1,5,8,6,3,7,

%T 2,4,1,3,6,8,2,4,9,7,5,1,3,6,8,10,5,9,2,4,7,1,3,5,7,9,11,2,4,6,8,10,1,

%U 3,5,8,10,12,6,11,2,7,9,4,1,3,5,2,9,12,10

%N Triangular array T(n,k) (n >= 1, 1 <= k <= n) read by rows: row n gives the lexicographically earliest solution to the n queens problem, or n zeros if no solution exists. The k-th queen is placed in square (k, T(n, k)).

%C Two further puzzle solutions were added to this sequence in November 2011; for board size 46x46 (a new solution) and for board size 47x47. The new puzzle solution for the 46x46 board was independently discovered by _Matthias Engelhardt_ on Apr 30 2011. The solution for the 47x47 board was discovered by _Colin S. Pearson_ on Jan 09 2008, but 47x47 can now be included in this sequence because the new 46x46 solution makes 47x47 contiguous with all previous solutions herein. The main contributer for this sequence can be contacted via a 'feedback' form at http://queens.cspea.co.uk/

%H Colin S. Pearson, <a href="/A141843/b141843.txt">Table of n, a(n) for n = 1..1128</a>

%H Matthias R. Engelhardt, <a href="http://nqueens.de/sub/SearchAlgorithm.en.html">The old nQueens problem</a>

%H Colin S. Pearson, <a href="http://queens.cspea.co.uk/">CSP Queens - Counting Queen-placements</a>

%H Martin S. Pearson, <a href="http://queens.lyndenlea.info/">Queens On A Chessboard</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens Puzzle</a>

%F lim {n->infinity} Sum {k=1..n} T(n,k)*x^k = A065188(x).

%e Triangle begins:

%e n\k [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

%e [1] 1;

%e [2] 0, 0;

%e [3] 0, 0, 0;

%e [4] 2, 4, 1, 3;

%e [5] 1, 3, 5, 2, 4;

%e [6] 2, 4, 6, 1, 3, 5;

%e [7] 1, 3, 5, 7, 2, 4, 6;

%e [8] 1, 5, 8, 6, 3, 7, 2, 4;

%e [9] 1, 3, 6, 8, 2, 4, 9, 7, 5;

%e [10] 1, 3, 6, 8, 10, 5, 9, 2, 4, 7;

%e [11] 1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10;

%e [12] 1, 3, 5, 8, 10, 12, 6, 11, 2, 7, 9, 4;

%e [13] ...

%e For n=8 the lexicographically smallest solution for the 8-queens problem is 1,5,8,6,3,7,2,4.

%Y Cf. A140450, A000170.

%K nonn,tabl

%O 1,7

%A _Colin S. Pearson_

%E We extended this sequence by adding new terms 1036 to 1128 relating to two further puzzle solutions; for board size 46x46 (a new solution) and for board size 47x47. Given that the k-th queen is placed in square (k, a(n, k)), we have added the terms (1, a(46, 1)) to (47, a(47, 47)).

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Last modified January 24 04:31 EST 2018. Contains 298115 sequences.