A352241 Maximal number of nonattacking black-square queens on an n X n chessboard.

1, 1, 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 44, 44, 45, 46, 47

Offset

1,4

Links

Table of n, a(n) for n=1..60.

Andy Huchala, Illustration for n = 52.

Andy Huchala, Python program.

Math StackExchange, Black queens on n X n board, 2022.

Formula

Conjecture: a(5k)=4k-1, a(5k+1)=4k, a(5k+2)=4k+1, a(5k+3)=4k+1, a(5k+4)=4k+2. [This does not hold for n = 52 and n = 57. - Andy Huchala, Apr 02 2024]

a(n) = A053757(n-1), at least for 1 <= n <= 12. [This is unlikely to continue. - N. J. A. Sloane, Mar 11 2022] [Indeed the equality does not hold for n=13. - Martin Ehrenstein, Mar 11 2022]

a(n+1) >= a(n); a(2n) = A352426(2n). - Martin Ehrenstein, Mar 23 2022

Crossrefs

Cf. A030978, A053757, A190394, A191236, A274616, A274933.

Cf. this sequence (maximal number for black-squares), A352325 (black-squares counts), A352426 (maximal number for white-squares), A352599 (white-squares counts).

Sequence in context: A172103 A123731 A247973 * A195181 A003005 A332204

Adjacent sequences: A352238 A352239 A352240 * A352242 A352243 A352244

Keyword

nonn,hard,more

Author

George Baloglou, Mar 09 2022

Extensions

a(13)-a(26) from Martin Ehrenstein, Mar 11 2022

a(27)-a(28) from Martin Ehrenstein, Mar 15 2022

a(29)-a(30) from Martin Ehrenstein, Mar 23 2022

a(31)-a(60) from Andy Huchala, Mar 27 2024

Status

approved