cp's OEIS Frontend

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

%I A374934 #35 Oct 30 2024 08:07:20
%S A374934 16,25,36,49,62,76,92,104,120,136,152,168,184,200,216
%N A374934 Maximum number of squares covered (i.e., attacked) by 4 independent (i.e., nonattacking) queens on an n X n chessboard.
%e A374934 4 X 4:
%e A374934   x Q x x
%e A374934   x x x Q
%e A374934   Q x x x
%e A374934   x x Q x
%e A374934 5 X 5 there are several arrangements:
%e A374934   x Q x x x
%e A374934   x x x x x
%e A374934   x x x x Q
%e A374934   Q x x x x
%e A374934   x x x Q x
%e A374934 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):
%e A374934   . . . . . . .
%e A374934   x x x x Q x .
%e A374934   Q x x x x x .
%e A374934   x x x x x x .
%e A374934   x x x x x Q .
%e A374934   x Q x x x x .
%e A374934 8 X 8: queens all knight-1,4 apart;
%e A374934 8 X 8 has 2 o/s;
%e A374934 9 X 9 has 5 o/s;
%e A374934 10 X 10 has 8 o/s;
%e A374934   o x x x x x x x x o
%e A374934   x o x x x x x x o x
%e A374934   x x x Q x x x x x x
%e A374934   x x x x x x x Q x x
%e A374934   x x x x x x x x x x
%e A374934   x x x x x x x x x x
%e A374934   x x Q x x x x x x x
%e A374934   x x x x x x Q x x x
%e A374934   x o x x x x x x o x
%e A374934   o x x x x x x x x o
%e A374934 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.
%e A374934   o x x o o x x x x o o x x o x
%e A374934   x o x x o x x x x o x x o x x
%e A374934   x x o x x x x x x x x o x x o
%e A374934   o x x o x x x x x x o x x o o
%e A374934   o o x x o x x x x o x x o o o
%e A374934   x x x x x x Q x x x x x x x x
%e A374934   x x x x x x x x Q x x x x x x
%e A374934   x x x x x Q x x x x x x x x x
%e A374934   x x x x x x x Q x x x x x x x
%e A374934   o o x x o x x x x o x x o o o
%e A374934   o x x o x x x x x x o x x o o
%e A374934   x x o x x x x x x x x o x x o
%e A374934   x o x x o x x x x o x x o x x
%e A374934   o x x o o x x x x o o x x o x
%e A374934   x x o o o x x x x o o o x x o
%Y A374934 Column 4 of A376732.
%Y A374934 Cf. A017113, A047461, A374933, A375116, A374935, A374936, A374937, A374938.
%K A374934 nonn,more
%O A374934 4,1
%A A374934 _John King_, Aug 08 2024
%E A374934 a(18) added using data from _Mia Muessig_ by _Andrew Howroyd_, Oct 05 2024