A181499 Triangle read by rows: number of solutions of n queens problem for given n and given number of conflicts.

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 28, 0, 0, 8, 4, 0, 0, 0, 0, 0, 64, 0, 28, 0, 0, 0, 0, 0, 0, 232, 0, 96, 24, 0, 0, 0, 0, 0, 0, 240, 0, 372, 112, 0, 0, 0, 0, 0, 88, 0, 0, 328, 1252, 872, 140, 0, 0, 0, 0, 0, 0, 0, 0, 3016, 5140, 4696, 1316, 32, 0, 0, 0, 0, 0

Offset: 0

Author

Matthias Engelhardt, Oct 25 2010

Keywords

• nonn
• tabl

Examples

			For n=4, there are only the two solutions 2-4-1-3 and 3-1-4-2. Both have two conflicts So the terms for n=4 are 0 (0 solutions for n=4 having 0 conflicts), 0, 2 (the two cited above), 0 and 0. These are members 10 to 15 of the sequence.
		

Links

• Matthias Engelhardt, Table of n, a(n) for n = 0..152 (corrected by Michel Marcus, Jan 19 2019)
• M. Engelhardt, Conflicts in the n-queens problem
• M. 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.

Crossrefs

Cf. A000170, A007705, A181500, A181501, A181502.

Formula

Row sum = A000170 (number of n queens placements)

Column 0 has same values as A007705 (torus n queens solutions)

Column 1 is always zero.