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A146303
Number of distinct ways to place queens (even fewer than n) on an n X n chessboard so that no queen is attacking another and that it is not possible to add another queen.
2
1, 4, 9, 18, 58, 348, 1862, 10188, 57600, 376692, 2640422, 19469324, 151978440, 1258451524, 10963084588, 100087600184
OFFSET
1,2
COMMENTS
In other words, number of maximal independent vertex sets (and minimal vertex covers) in the n X n queen graph. - Eric W. Weisstein, Jun 20 2017
LINKS
S. W. Golomb and L. D. Baumert, Backtrack Programming, Journal of the ACM, 4 (2001), 516-524.
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
Eric Weisstein's World of Mathematics, Minimal Vertex Cover
Eric Weisstein's World of Mathematics, Queen Graph
EXAMPLE
The a(2) = 4 solutions are to place a single queen in each of the squares of the chessboard. For n=3, there is a single one-queen solution (placing the queen in b2) and eight two-queen solutions, but no three-queen solution (see A000170).
CROSSREFS
Sequence in context: A074896 A015713 A049198 * A344999 A203205 A330375
KEYWORD
hard,nonn,more
AUTHOR
Paolo Bonzini, Oct 29 2008
EXTENSIONS
a(12)-a(16) from Stefan Kral, Aug 10 2016
STATUS
approved