A261596 - OEIS

%I #15 Sep 15 2015 15:34:30

%S 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,

%T 4,6,2,4,9,7,5,3,1,6,8,2,4,6,8,10,1,3,5,7,9

%N 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)).

%C See the comments under A260319.

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

%e 1 <= n < 6: no symmetric solutions exist.

%e n = 6: 246135 is the first and only symmetric solution.

%e        .*....

%e        ...*..

%e        .....*

%e        *.....

%e        ..*...

%e        ....*.

%e n = 7: 2514736 is the first of two existing symmetric solutions.

%e n = 8: 35281746 is the first and only symmetric solution.

%e Triangle starts:

%e 0;

%e 0, 0;

%e 0, 0, 0;

%e 0, 0, 0, 0;

%e 0, 0, 0, 0, 0;

%e 2, 4, 6, 1, 3, 5;

%e 2, 5, 1, 4, 7, 3, 6;

%e 3, 5, 2, 8, 1, 7, 4, 6;

%e ...

%Y Cf. A141843, A260319, A261595, A261597.

%K nonn,tabl

%O 1,16

%A _Martin Renner_, Aug 25 2015