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A374013
n-queens completion threshold. The maximum number such that placing a(n) or fewer mutually non-attacking queens on an n X n chessboard is always completeable to a full n-queen configuration.
0
0, 1, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
OFFSET
4,7
COMMENTS
For n large enough, n/60 <= a(n) <= 0.241*n [Glock et al.].
LINKS
I. P. Gent, C. A. Jefferson, and P. W. Nightingale, Complexity of n-Queens Completion, Journal of Artificial Intelligence Research, 59, 815-848.
S. Glock, D. M. Correia, and B. Sudakov, The n-queens completion problem, Res Math Sci, 9 (2022), 41.
Hugo M. Nielsen, C implementation
EXAMPLE
There are 2 solutions to the 4-queens problem:
. Q . .
. . . Q
Q . . .
. . Q .
and
. . Q .
Q . . .
. . . Q
. Q . .
Neither of these has a queen in the upper left corner, so placing a queen here will definitely make the configuration non-completable, while placing no queens is completable, see the two examples.
PROG
(C) \\ see github link
CROSSREFS
Cf. A000170.
Sequence in context: A165116 A111656 A165118 * A342882 A025423 A284263
KEYWORD
nonn,more
AUTHOR
Hugo M. Nielsen, Jun 25 2024
STATUS
approved