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

1,7

Comments

See the comments under A260318.

References

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

Links

Table of n, a(n) for n=1..66.

Example

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;
...

Crossrefs

Cf. A141843, A260318, A261596, A261597.

Sequence in context: A322169 A332084 A130266 * A211197 A258246 A258240

Adjacent sequences: A261592 A261593 A261594 * A261596 A261597 A261598

Keyword

nonn,tabl

Author

Martin Renner, Aug 25 2015

Status

approved