A261596 -id:A261596 - cp's OEIS frontend

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

Martin Renner, Aug 25 2015

See the comments under A260318.

			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;
...

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

Cf. A141843, A260318, A261596, A261597.

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)).

Original entry on oeis.org

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

Martin Renner, Aug 25 2015

See the comments under A260320.

			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;
...

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

Cf. A141843, A260320, A261595, A261596.

cp's OEIS Frontend

Views

Author

Keywords

Comments

Examples

References

Crossrefs