A319236 The profile of the backtrack tree for the sixteen queens problem.

1, 16, 210, 2236, 19688, 141812, 838816, 3998456, 15324708, 46358876, 108478966, 193892860, 260303408, 253897632, 171158018, 72002088, 14772512

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 sixteen queens problem 1141190303 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..16.

Wikipedia, Backtracking

Wikipedia, Eight queens puzzle

Formula

a(16) = A000170(16), the number of solutions.

Crossrefs

Cf. A000170, A319235.

Sequence in context: A283694 A283126 A295712 * A222447 A059385 A009440

Adjacent sequences: A319233 A319234 A319235 * A319237 A319238 A319239

Keyword

nonn,fini,full

Author

Peter Luschny, Sep 15 2018

Status

approved