A374934 Maximum number of squares covered (i.e., attacked) by 4 independent (i.e., nonattacking) queens on an n X n chessboard.

16, 25, 36, 49, 62, 76, 92, 104, 120, 136, 152, 168, 184, 200, 216

Offset: 4

Author

John King, Aug 08 2024

Keywords

• nonn
• more

Examples

			4 X 4:
  x Q x x
  x x x Q
  Q x x x
  x x Q x
5 X 5 there are several arrangements:
  x Q x x x
  x x x x x
  x x x x Q
  Q x x x x
  x x x Q x
6 X 6 and 7 X 7 (add a row and column) pattern as 4 queens knight-1,3 and 1,4 separation (not symmetric):
  . . . . . . .
  x x x x Q x .
  Q x x x x x .
  x x x x x x .
  x x x x x Q .
  x Q x x x x .
8 X 8: queens all knight-1,4 apart;
8 X 8 has 2 o/s;
9 X 9 has 5 o/s;
10 X 10 has 8 o/s;
  o x x x x x x x x o
  x o x x x x x x o x
  x x x Q x x x x x x
  x x x x x x x Q x x
  x x x x x x x x x x
  x x x x x x x x x x
  x x Q x x x x x x x
  x x x x x x Q x x x
  x o x x x x x x o x
  o x x x x x x x x o
beyond 10 X 10, the 4 queens separated as 1,2 knights begins to be the best layout; at 15 X 15, the pattern is clear.
  o x x o o x x x x o o x x o x
  x o x x o x x x x o x x o x x
  x x o x x x x x x x x o x x o
  o x x o x x x x x x o x x o o
  o o x x o x x x x o x x o o o
  x x x x x x Q x x x x x x x x
  x x x x x x x x Q x x x x x x
  x x x x x Q x x x x x x x x x
  x x x x x x x Q x x x x x x x
  o o x x o x x x x o x x o o o
  o x x o x x x x x x o x x o o
  x x o x x x x x x x x o x x o
  x o x x o x x x x o x x o x x
  o x x o o x x x x o o x x o x
  x x o o o x x x x o o o x x o
		

Crossrefs

Column 4 of A376732.

Cf. A017113, A047461, A374933, A375116, A374935, A374936, A374937, A374938.

Extensions

a(18) added using data from Mia Muessig by Andrew Howroyd, Oct 05 2024