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A352241 Maximal number of nonattacking black-square queens on an n X n chessboard.

%I A352241 #100 Apr 02 2024 07:35:46
%S A352241 1,1,1,2,3,4,5,5,6,7,8,9,9,10,11,12,13,13,14,15,16,17,17,18,19,20,21,
%T A352241 21,22,23,24,25,25,26,27,28,29,29,30,31,32,33,33,34,35,36,37,37,38,39,
%U A352241 40,40,41,42,43,44,44,45,46,47
%N A352241 Maximal number of nonattacking black-square queens on an n X n chessboard.
%H A352241 Andy Huchala, <a href="/A352241/a352241_1.png">Illustration for n = 52</a>.
%H A352241 Andy Huchala, <a href="/A352241/a352241.py.txt">Python program</a>.
%H A352241 Math StackExchange, <a href="https://math.stackexchange.com/questions/4397136/black-queens-on-n-times-n-board">Black queens on n X n board</a>, 2022.
%F A352241 Conjecture: a(5k)=4k-1, a(5k+1)=4k, a(5k+2)=4k+1, a(5k+3)=4k+1, a(5k+4)=4k+2. [This does not hold for n = 52 and n = 57. - _Andy Huchala_, Apr 02 2024]
%F A352241 a(n) = A053757(n-1), at least for 1 <= n <= 12. [This is unlikely to continue. - _N. J. A. Sloane_, Mar 11 2022] [Indeed the equality does not hold for n=13. - _Martin Ehrenstein_, Mar 11 2022]
%F A352241 a(n+1) >= a(n); a(2n) = A352426(2n). - _Martin Ehrenstein_, Mar 23 2022
%Y A352241 Cf. A030978, A053757, A190394, A191236, A274616, A274933.
%Y A352241 Cf. this sequence (maximal number for black-squares), A352325 (black-squares counts), A352426 (maximal number for white-squares), A352599 (white-squares counts).
%K A352241 nonn,hard,more
%O A352241 1,4
%A A352241 _George Baloglou_, Mar 09 2022
%E A352241 a(13)-a(26) from _Martin Ehrenstein_, Mar 11 2022
%E A352241 a(27)-a(28) from _Martin Ehrenstein_, Mar 15 2022
%E A352241 a(29)-a(30) from _Martin Ehrenstein_, Mar 23 2022
%E A352241 a(31)-a(60) from _Andy Huchala_, Mar 27 2024