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%I #19 Sep 16 2015 03:47:42
%S 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,
%T 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
%N 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)).
%C See the comments under A260318.
%D Maurice Kraitchik: Mathematical Recreations. Mineola, NY: Dover, 2nd ed. 1953, pp. 247-255 (The Problem of the Queens).
%e n = 1: 1 is the trivial solution.
%e 2 <= n < 4: no doubly centro-symmetric solutions exist.
%e n = 4: 2413 is the first and only solution.
%e .*..
%e ...*
%e *...
%e ..*.
%e n = 5: 25314 is the first and only solution.
%e 6 <= n < 12: no doubly centro-symmetric solutions exist.
%e Triangle starts:
%e 1;
%e 0, 0;
%e 0, 0, 0;
%e 2, 4, 1, 3;
%e 2, 5, 3, 1, 4;
%e 0, 0, 0, 0, 0, 0;
%e ...
%Y Cf. A141843, A260318, A261596, A261597.
%K nonn,tabl
%O 1,7
%A _Martin Renner_, Aug 25 2015
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