A352241 - OEIS

%I #100 Apr 02 2024 07:35:46

%S 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 21,22,23,24,25,25,26,27,28,29,29,30,31,32,33,33,34,35,36,37,37,38,39,

%U 40,40,41,42,43,44,44,45,46,47

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

%H Andy Huchala, <a href="/A352241/a352241_1.png">Illustration for n = 52</a>.

%H Andy Huchala, <a href="/A352241/a352241.py.txt">Python program</a>.

%H 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 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 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 a(n+1) >= a(n); a(2n) = A352426(2n). - _Martin Ehrenstein_, Mar 23 2022

%Y Cf. A030978, A053757, A190394, A191236, A274616, A274933.

%Y Cf. this sequence (maximal number for black-squares), A352325 (black-squares counts), A352426 (maximal number for white-squares), A352599 (white-squares counts).

%K nonn,hard,more

%O 1,4

%A _George Baloglou_, Mar 09 2022

%E a(13)-a(26) from _Martin Ehrenstein_, Mar 11 2022

%E a(27)-a(28) from _Martin Ehrenstein_, Mar 15 2022

%E a(29)-a(30) from _Martin Ehrenstein_, Mar 23 2022

%E a(31)-a(60) from _Andy Huchala_, Mar 27 2024