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A376732
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.
7
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, 49, 49, 49, 28, 44, 55, 62, 64, 64, 64, 64, 33, 52, 66, 76, 81, 81, 81, 81, 81, 36, 60, 77, 92, 100, 100, 100, 100, 100, 100, 41, 68, 88, 104, 121, 121, 121, 121, 121, 121, 121
OFFSET
1,2
COMMENTS
T(2,2) = T(3,3) = 0 indicate that there are no solutions to the n-queens problem when n is 2 or 3.
FORMULA
T(n,k) = n^2 for k >= A075324(n), n >= 4.
EXAMPLE
Triangle begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12
----+-----------------------------------------------------------
1 | 1;
2 | 4, 0;
3 | 9, 9, 0;
4 | 12, 15, 16, 16;
5 | 17, 23, 25, 25, 25;
6 | 20, 30, 35, 36, 36, 36;
7 | 25, 37, 45, 49, 49, 49, 49;
8 | 28, 44, 55, 62, 64, 64, 64, 64;
9 | 33, 52, 66, 76, 81, 81, 81, 81, 81;
10 | 36, 60, 77, 92, 100, 100, 100, 100, 100, 100;
11 | 41, 68, 88, 104, 121, 121, 121, 121, 121, 121, 121;
12 | 44, 76, 101, 120, 134, 142, 144, 144, 144, 144, 144, 144;
13 | 49, 84, 112, 136, 153, 165, 169, 169, 169, 169, 169, ...;
14 | 52, 92, 125, 152, 172, 186, 194, 196, 196, 196, 196, ...;
15 | 57, 100, 136, 168, 193, 209, 221, 224, 225, 225, 225, ...;
16 | 60, 108, 149, 184, 212, 231, 242, 251, 256, 256, 256, ...;
17 | 65, 116, 160, 200, 233, 255, 269, 281, 289, 289, 289, ...;
18 | 68, 124, 173, 216, 252, 277, 294, 310, 322, 324, 324, ...;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
John King, Oct 03 2024
EXTENSIONS
Initial terms by John King and Mia Müßig added by Mia Muessig, Oct 05 2024
STATUS
approved