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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
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, 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, 3, 5, 8, 10, 12, 6, 11, 2, 7, 9, 4, 1, 3, 5, 2, 9, 12, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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/

LINKS

Colin S. Pearson, Table of n, a(n) for n = 1..1128

Matthias R. Engelhardt, The old nQueens problem

Colin S. Pearson, CSP Queens - Counting Queen-placements

Martin S. Pearson, Queens On A Chessboard

Wikipedia, Eight Queens Puzzle

FORMULA

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

EXAMPLE

Triangle begins:

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

[1]  1;

[2]  0,   0;

[3]  0,   0,   0;

[4]  2,   4,   1,   3;

[5]  1,   3,   5,   2,   4;

[6]  2,   4,   6,   1,   3,   5;

[7]  1,   3,   5,   7,   2,   4,   6;

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

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

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

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

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

[13] ...

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

CROSSREFS

Cf. A140450, A000170.

Sequence in context: A254076 A257164 A190555 * A130266 A261595 A211197

Adjacent sequences:  A141840 A141841 A141842 * A141844 A141845 A141846

KEYWORD

nonn,tabl

AUTHOR

Colin S. Pearson

EXTENSIONS

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)).

STATUS

approved

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Last modified September 24 04:27 EDT 2017. Contains 292403 sequences.