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Maximal number of unattacked squares with n queens on n X n board (answers for n >= 17 only probable).
3

%I #34 Sep 03 2021 13:58:37

%S 0,0,0,1,3,5,7,11,18,22,30,36,47,56,72,82,97,111,132,145,170,186,216,

%T 240,260,290,324,360,381,420

%N Maximal number of unattacked squares with n queens on n X n board (answers for n >= 17 only probable).

%H Yanan Jiang and Steven J. Miller, <a href="https://arxiv.org/abs/2010.14990">Generalizing Ruth-Aaron Numbers</a>, arXiv:2010.14990 [math.NT], 2020; <a href="https://journals.calstate.edu/pump/article/view/2458">published</a> in The Pump Journal of Undergraduate Research, 4 (2021), 20-62. [That paper references this sequence entry, probably by mistake; cf. A039752.]

%H Bernard Lemaire and Pavel Vitushinkiy, <a href="http://www.ffjm.org/upload/fichiers/N_NON_DOMINATING_QUEENS.pdf">Placing n non dominating queens on the n X n chessboard. Part I</a>, French Federation of Mathematical Games.

%H Bernard Lemaire and Pavel Vitushinkiy, <a href="https://www.ffjm.org/upload/fichiers/THE_PROBLEM_OF_N_NON_DOMINATING_part_II.pdf">Placing n non dominating queens on the n X n chessboard. Part II</a>, French Federation of Mathematical Games.

%H Steven J. Miller, Haoyu Sheng, and Daniel Turek, <a href="https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/Rooks30.pdf">When rooks miss: probability through chess</a>, Williams College (2020).

%H Mario Velucchi, <a href="https://web.archive.org/web/20090226224221/http://www.cli.di.unipi.it/~velucchi/queens.txt">NON-Dominating Queens Problem</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QueensProblem.html">Queens Problem.</a>

%Y Cf. A019317, A274947.

%K nonn,more

%O 1,5

%A Mario Velucchi (mathchess(AT)velucchi.it)