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

1,16

Comments

See the comments under A260319.

References

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

Links

Table of n, a(n) for n=1..55.

Example

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;
...

Crossrefs

Cf. A141843, A260319, A261595, A261597.

Sequence in context: A187717 A125944 A077069 * A080413 A004517 A254350

Adjacent sequences: A261593 A261594 A261595 * A261597 A261598 A261599

Keyword

nonn,tabl

Author

Martin Renner, Aug 25 2015

Status

approved