A261595 Triangular array T(n, k) read by rows (n >= 1, 1 <= k <= n): row n gives the lexicographically earliest doubly centro-symmetric characteristic solution to the n queens problem, or n zeros if no doubly centro-symmetric characteristic solution exists. The k-th queen is placed in square (k, T(n, k)).

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

Offset: 1

Author

Martin Renner, Aug 25 2015

Keywords

• nonn
• tabl

Comments

See the comments under A260318.

Examples

			n = 1: 1 is the trivial solution.
2 <= n < 4: no doubly centro-symmetric solutions exist.
n = 4: 2413 is the first and only solution.
       .*..
       ...*
       *...
       ..*.
n = 5: 25314 is the first and only solution.
6 <= n < 12: no doubly centro-symmetric solutions exist.
Triangle starts:
1;
0, 0;
0, 0, 0;
2, 4, 1, 3;
2, 5, 3, 1, 4;
0, 0, 0, 0, 0, 0;
...
		

References

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

Crossrefs

Cf. A141843, A260318, A261596, A261597.