%I #17 Oct 09 2019 20:57:15
%S 1,8,42,140,344,568,550,312,92
%N The profile of the backtrack tree for the eight queens problem.
%C The profile (p_0, p_1, ..., p_n) is the number of nodes at each level of the tree.
%C The backtrack tree as defined by Knuth has for the eight queens problem 2057 nodes.
%D D. E. Knuth, The Art of Computer Programming, Volume 4, Pre-fascicle 5B, Introduction to Backtracking, 7.2.2. Backtrack programming. 2018.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Backtracking">Backtracking</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight queens puzzle</a>
%F a(8) = A000170(8), the number of solutions.
%Y Cf. A000170, A319236.
%K nonn,fini,full
%O 0,2
%A _Peter Luschny_, Sep 15 2018