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

0,13

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.

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.

Example

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.

Crossrefs

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

Sequence in context: A350487 A258759 A350793 * A010893 A181501 A213704

Adjacent sequences: A181496 A181497 A181498 * A181500 A181501 A181502

Keyword

nonn,tabl

Author

Matthias Engelhardt, Oct 25 2010

Status

approved