A319235 The profile of the backtrack tree for the eight queens problem.

1, 8, 42, 140, 344, 568, 550, 312, 92

Offset

0,2

Comments

The profile (p_0, p_1, ..., p_n) is the number of nodes at each level of the tree.

The backtrack tree as defined by Knuth has for the eight queens problem 2057 nodes.

References

D. E. Knuth, The Art of Computer Programming, Volume 4, Pre-fascicle 5B, Introduction to Backtracking, 7.2.2. Backtrack programming. 2018.

Links

Table of n, a(n) for n=0..8.

Wikipedia, Backtracking

Wikipedia, Eight queens puzzle

Formula

a(8) = A000170(8), the number of solutions.

Crossrefs

Cf. A000170, A319236.

Sequence in context: A292059 A027903 A231069 * A341764 A256861 A287221

Adjacent sequences: A319232 A319233 A319234 * A319236 A319237 A319238

Keyword

nonn,fini,full

Author

Peter Luschny, Sep 15 2018

Status

approved