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 A181500 Triangle read by rows: number of solutions of n queens problem for given n and given number of queens engaged in conflicts. 4
 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 28, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 64, 0, 28, 0, 0, 0, 0, 0, 0, 232, 8, 32, 48, 32 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,15 COMMENTS Schlude and Specker investigate if it is possible to set n-1 non-attacking queens on an n X n toroidal chessboard. That is equivalent to searching for normal (i.e., non-toroidal) solutions of 3 engaged queens. In this case, one of the three queens has conflicts with both other queens. If you remove this queen, you get a setting of n-1 queens without conflicts, i.e., a toroidal solution. LINKS M. Engelhardt, Rows n=0..16 of triangle, flattened Matthias Engelhardt, Conflicts in the n-queens problem Matthias Engelhardt, Conflict tables for the n-queens problem M. R. Engelhardt, A group-based search for solutions of the n-queens problem, Discr. Math., 307 (2007), 2535-2551. Konrad Schlude and Ernst Specker, Zum Problem der Damen auf dem Torus, Technical Report 412, Computer Science Department ETH Zurich, 2003. FORMULA Row sum = A000170 (number of n-queen placements). Column 0 has same values as A007705 (torus n-queen solutions). Columns 1 and 2 are always zero. Column 3 counts solutions of the special "Schlude-Specker" situation. EXAMPLE Triangle begins: 0; 1, 0; 0, 0, 0; 0, 0, 0, 0; 0, 0, 0, 0, 2; 10, 0, 0, 0, 0, 0; 0, 0, 0, 0, 4, 0, 0; 28, 0, 0, 0, 0, 0, 12, 0; ... - Andrew Howroyd, Dec 31 2017 For n=4, there are only the two solutions 2-4-1-3 and 3-1-4-2. For both solutions, all 4 queens are engaged in conflicts. So the terms for n=4 are 0 (0 solutions for n=4 having 0 engaged queens), 0, 0, 0 and 2 (the two cited above). These are members 11 to 15 of the sequence. CROSSREFS Cf. A181499, A181501, A181502. Sequence in context: A140319 A120314 A050924 * A189876 A189867 A189875 Adjacent sequences: A181497 A181498 A181499 * A181501 A181502 A181503 KEYWORD nonn,tabl AUTHOR Matthias Engelhardt, Oct 30 2010 EXTENSIONS Offset corrected by Andrew Howroyd, Dec 31 2017 STATUS approved

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Last modified August 13 10:15 EDT 2024. Contains 375130 sequences. (Running on oeis4.)