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)).

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

1,12

Comments

See the comments under A260320.

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..78.

Example

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;
...

Crossrefs

Cf. A141843, A260320, A261595, A261596.

Sequence in context: A272476 A205701 A218888 * A197331 A113475 A182743

Adjacent sequences: A261594 A261595 A261596 * A261598 A261599 A261600

Keyword

nonn,tabl

Author

Martin Renner, Aug 25 2015

Status

approved