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%I #30 Nov 07 2024 08:48:30
%S 1,4,0,9,9,0,12,15,16,16,17,23,25,25,25,20,30,35,36,36,36,25,37,45,49,
%T 49,49,49,28,44,55,62,64,64,64,64,33,52,66,76,81,81,81,81,81,36,60,77,
%U 92,100,100,100,100,100,100,41,68,88,104,121,121,121,121,121,121,121
%N Triangle read by rows: T(n,k) is the maximum number of squares covered (i.e., attacked) by k independent (i.e., non-attacking) queens on an n X n chessboard.
%C T(2,2) = T(3,3) = 0 indicate that there are no solutions to the n-queens problem when n is 2 or 3.
%H Mia Muessig, <a href="/A376732/b376732.txt">Table of n, a(n) for n = 1..240</a>
%H John King, <a href="/A376732/a376732.pdf">Examples for Queens 1,2,3,4,5 up to 11x11</a>.
%H John King, <a href="/A376732/a376732.jpg">Examples for Queens 6,7,8,9 up to 15x15</a>.
%H Mia Muessig, <a href="https://gist.github.com/PhoenixSmaug/18deba3e6cf140505b14ec27940038a9">Julia code to compute the sequence</a>
%F T(n,k) = n^2 for k >= A075324(n), n >= 4.
%e Triangle begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e ----+-----------------------------------------------------------
%e 1 | 1;
%e 2 | 4, 0;
%e 3 | 9, 9, 0;
%e 4 | 12, 15, 16, 16;
%e 5 | 17, 23, 25, 25, 25;
%e 6 | 20, 30, 35, 36, 36, 36;
%e 7 | 25, 37, 45, 49, 49, 49, 49;
%e 8 | 28, 44, 55, 62, 64, 64, 64, 64;
%e 9 | 33, 52, 66, 76, 81, 81, 81, 81, 81;
%e 10 | 36, 60, 77, 92, 100, 100, 100, 100, 100, 100;
%e 11 | 41, 68, 88, 104, 121, 121, 121, 121, 121, 121, 121;
%e 12 | 44, 76, 101, 120, 134, 142, 144, 144, 144, 144, 144, 144;
%e 13 | 49, 84, 112, 136, 153, 165, 169, 169, 169, 169, 169, ...;
%e 14 | 52, 92, 125, 152, 172, 186, 194, 196, 196, 196, 196, ...;
%e 15 | 57, 100, 136, 168, 193, 209, 221, 224, 225, 225, 225, ...;
%e 16 | 60, 108, 149, 184, 212, 231, 242, 251, 256, 256, 256, ...;
%e 17 | 65, 116, 160, 200, 233, 255, 269, 281, 289, 289, 289, ...;
%e 18 | 68, 124, 173, 216, 252, 277, 294, 310, 322, 324, 324, ...;
%e ...
%Y Columns 1..8 are A047461, A374933, A375116, A374934, A374935, A374936, A374937, A374938.
%Y Cf. A075324, A002567, A075458, A274947.
%K nonn,tabl
%O 1,2
%A _John King_, Oct 03 2024
%E Initial terms by John King and Mia Müßig added by _Mia Muessig_, Oct 05 2024