A352426 -id:A352426 - cp's OEIS frontend

A352599 Number of ways of placing A352426(n) nonattacking white-square queens on an n X n board.

1, 2, 4, 6, 2, 6, 64, 112, 68, 80, 32, 36, 28, 1414, 576, 384, 40, 70396, 40896, 22468, 9808, 1152, 252, 2246138, 482272, 185932

Offset: 1

Martin Ehrenstein, Mar 22 2022

Equivalently the number of ways of placing the maximal number of nonattacking black-square queens on an inverted n X n chessboard, that is a board with the a1 square white, the a2 and b1 squares black, etc.

Cf. A352241 (maximal number for black-squares), A352325 (black-squares counts), A352426 (maximal number for white-squares), this sequence (white-squares counts).

Python
```
See A352426.
```

a(2n) = A352325(2n).

a(21)-a(24) from Vaclav Kotesovec, Mar 23 2022

a(25)-a(26) from Vaclav Kotesovec, Apr 01 2022

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

Original entry on oeis.org

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

George Baloglou, Mar 09 2022

Andy Huchala, Illustration for n = 52.
Andy Huchala, Python program.
Math StackExchange, Black queens on n X n board, 2022.

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).

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

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

cp's OEIS Frontend

A352599 Number of ways of placing A352426(n) nonattacking white-square queens on an n X n board.

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