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

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, 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, 0, 0, 0, 0

Offset: 0

Author

Matthias Engelhardt, Oct 30 2010

Keywords

• nonn
• tabl

Comments

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.

Examples

			Triangle begins:
   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, 0, 0, 0;
  ... - _Andrew Howroyd_, Dec 31 2017
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.
		

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.

Crossrefs

Cf. A000170, A007705, A181499, A181500, A181502.

Formula

Row sum =A000170 (number of n queens placements)

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

Extensions

Offset corrected by Andrew Howroyd, Dec 31 2017