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A181501 Triangle read by rows: number of solutions of n queens problem for given n and given number of connection components of conflict constellation.

%I A181501 #21 Jul 22 2025 08:41:47
%S A181501 0,1,0,0,0,0,0,0,0,0,0,0,2,0,0,10,0,0,0,0,0,0,4,0,0,0,0,0,28,0,4,8,0,
%T A181501 0,0,0,0,0,92,0,0,0,0,0,0,0,8,272,56,16,0,0,0,0,0,0,96,344,240,44,0,0,
%U A181501 0,0,0,0
%N A181501 Triangle read by rows: number of solutions of n queens problem for given n and given number of connection components of conflict constellation.
%C A181501 The rightmost part of the triangle contains only zeros. As any connection component needs at least two queens, the number of connection components of a solution is always less than or equal to n.
%H A181501 M. Engelhardt, <a href="/A181501/b181501.txt">Rows n=0..16 of triangle, flattened</a>
%H A181501 Matthias Engelhardt, <a href="http://nqueens.de/sub/Conflicts.en.html">Conflicts in the n-queens problem</a>
%H A181501 Matthias Engelhardt, <a href="http://nqueens.de/sub/ConflictTables.en.html">Conflict tables for the n-queens problem</a>
%H A181501 M. R. Engelhardt, <a href="http://dx.doi.org/10.1016/j.disc.2007.01.007">A group-based search for solutions of the n-queens problem</a>, Discr. Math., 307 (2007), 2535-2551.
%F A181501 Row sum =A000170 (number of n queens placements)
%F A181501 Column 0 has same values as A007705 (torus n queens solutions)
%e A181501 Triangle begins:
%e A181501    0;
%e A181501    1, 0;
%e A181501    0, 0, 0;
%e A181501    0, 0, 0, 0;
%e A181501    0, 0, 2, 0, 0;
%e A181501   10, 0, 0, 0, 0, 0;
%e A181501    0, 4, 0, 0, 0, 0, 0;
%e A181501   28, 0, 4, 8, 0, 0, 0, 0;
%e A181501   ... - _Andrew Howroyd_, Dec 31 2017
%e A181501 for n=4, there are only the two solutions 2-4-1-3 and 3-1-4-2. Both have two connection components in the conflicts graph. So, the terms for n=4 are 0, 0, 2 (the two cited above), 0 and 0. These are members 10 to 15 of the sequence.
%Y A181501 Cf. A000170, A007705, A181499, A181500, A181502.
%K A181501 nonn,tabl
%O A181501 0,13
%A A181501 _Matthias Engelhardt_, Oct 30 2010
%E A181501 Offset corrected by _Andrew Howroyd_, Dec 31 2017