A261596 Triangular array T(n, k) read by rows (n >= 1, 1 <= k <= n): row n gives the lexicographically earliest symmetric characteristic solution to the n queens problem, or n zeros if no symmetric 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, 0, 0, 0, 0, 0, 2, 4, 6, 1, 3, 5, 2, 5, 1, 4, 7, 3, 6, 3, 5, 2, 8, 1, 7, 4, 6, 2, 4, 9, 7, 5, 3, 1, 6, 8, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9

Offset: 1

Author

Martin Renner, Aug 25 2015

Keywords

• nonn
• tabl

Comments

See the comments under A260319.

Examples

			1 <= n < 6: no symmetric solutions exist.
n = 6: 246135 is the first and only symmetric solution.
       .*....
       ...*..
       .....*
       *.....
       ..*...
       ....*.
n = 7: 2514736 is the first of two existing symmetric solutions.
n = 8: 35281746 is the first and only symmetric solution.
Triangle starts:
0;
0, 0;
0, 0, 0;
0, 0, 0, 0;
0, 0, 0, 0, 0;
2, 4, 6, 1, 3, 5;
2, 5, 1, 4, 7, 3, 6;
3, 5, 2, 8, 1, 7, 4, 6;
...
		

References

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

Crossrefs

Cf. A141843, A260319, A261595, A261597.