A375116 - OEIS

A375116

Maximum number of squares covered (i.e., attacked) by 3 independent (i.e., nonattacking) queens on an n X n chessboard.

16, 25, 35, 45, 55, 66, 77, 88, 101, 112, 125, 136, 149, 160, 173, 184, 197, 208, 221, 232, 245, 256, 269, 280, 293, 304, 317, 328, 341, 352, 365, 376, 389, 400, 413, 424, 437, 448, 461, 472, 485, 496, 509, 520, 533, 544, 557, 568, 581, 592, 605, 616, 629, 640, 653, 664, 677

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,1

COMMENTS

It is not possible to place 3 independent queens on a 1 X 1 or 2 X 2 or 3 X 3 board.

There is a related sequence of 'uncovered' squares i.e., n^2 - a(n).

There is another sequence denoting the potency of the new queen a(n) - A374933(n).

LINKS

Table of n, a(n) for n=4..60.

FORMULA

a(n) = 12*n - 43 - (n mod 2) for n >= 10.

EXAMPLE

4 X 4 complete coverage with 3 queens

x x x x

x Q x x

x x x Q

Q x x x

5 X 5 complete coverage with 3 queens

Q x x x x

x x x x x

x x x Q x

x x x x x

x x Q x x

6 X 6 incomplete 1 o/s

x x x x o x

Q x x x x x

x x x x x Q

x x x x x x

x x Q x x x

x x x x x x

6 X 6 coverage complete but NOT independent

Q 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 q x x x

x x x x x x

7 X 7 best leaves 4 o/s (same layout as 6 X 6 with extra row and column)

There are alternative layouts - how many is not identified.

x x x x o 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 Q x x x x

x x x x x x o

x x x o x x o

CROSSREFS

Column 3 of A376732.

Cf. A047461 (for one queen), A374933 (for two queens), A374934, A374935, A374936.

Sequence in context: A176512 A001033 A100647 * A374934 A245371 A235717

Adjacent sequences: A375113 A375114 A375115 * A375117 A375118 A375119

KEYWORD

nonn

AUTHOR

John King, Jul 30 2024

EXTENSIONS

a(6)-a(8) corrected by John King, Sep 17 2024

a(9) corrected using data from Mia Muessig by Andrew Howroyd, Oct 05 2024

STATUS

approved