A261597 Triangular array T(n, k) read by rows (n >= 1, 1 <= k <= n): row n gives the lexicographically earliest asymmetric characteristic solution to the n queens problem, or n zeros if no asymmetric characteristic solution exists. The k-th queen is placed in square (k, T(n, k)).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 2, 4, 0, 0, 0, 0, 0, 0, 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

Offset: 1

Author

Martin Renner, Aug 25 2015

Keywords

• nonn
• tabl

Comments

See the comments under A260320.

Examples

			1 <= n < 5: no ordinary solutions exist.
n = 5: 13524 is the first and only solution.
       *....
       ..*..
       ....*
       .*...
       ...*.
n = 6: no ordinary solution exists.
n = 7: 1357246 is the first of four existing solutions.
n = 8: 15863724 is the first of eleven existing solutions.
Triangle starts:
0;
0, 0;
0, 0, 0;
0, 0, 0, 0;
1, 3, 5, 2, 4;
0, 0, 0, 0, 0, 0;
1, 3, 5, 7, 2, 4, 6;
1, 5, 8, 6, 3, 7, 2, 4;
...
		

References

• Maurice Kraitchik: Mathematical Recreations. Mineola, NY: Dover, 2nd ed. 1953, p. 247-255 (The Problem of the Queens).

Crossrefs

Cf. A141843, A260320, A261595, A261596.