A348129 Number T(n,k) of ways to place k nonattacking queens on an n X n board; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 1, 1, 1, 4, 0, 1, 9, 8, 0, 1, 16, 44, 24, 2, 1, 25, 140, 204, 82, 10, 1, 36, 340, 1024, 982, 248, 4, 1, 49, 700, 3628, 7002, 4618, 832, 40, 1, 64, 1288, 10320, 34568, 46736, 22708, 3192, 92, 1, 81, 2184, 25096, 131248, 310496, 312956, 119180, 13848, 352, 1, 100, 3480, 54400, 412596, 1535440, 2716096, 2119176, 636524, 56832, 724

Offset: 0

Author

Alois P. Heinz, Oct 01 2021

Keywords

• nonn
• tabl
• hard

Examples

			T(3,2) = 8:
  .-----. .-----. .-----. .-----. .-----. .-----. .-----. .-----.
  |Q . .| |Q . .| |. . Q| |. . Q| |. . .| |. Q .| |. Q .| |. . .|
  |. . Q| |. . .| |. . .| |Q . .| |Q . .| |. . .| |. . .| |. . Q|
  |. . .| |. Q .| |. Q .| |. . .| |. . Q| |. . Q| |Q . .| |Q . .|
  `-----´ `-----´ `-----´ `-----´ `-----´ `-----´ `-----´ `-----´.
Triangle T(n,k) begins:
  1;
  1,  1;
  1,  4,    0;
  1,  9,    8,     0;
  1, 16,   44,    24,      2;
  1, 25,  140,   204,     82,     10;
  1, 36,  340,  1024,    982,    248,      4;
  1, 49,  700,  3628,   7002,   4618,    832,     40;
  1, 64, 1288, 10320,  34568,  46736,  22708,   3192,    92;
  1, 81, 2184, 25096, 131248, 310496, 312956, 119180, 13848, 352;
  ...
		

Crossrefs

Columns k=0-8 give: A000012, A000290, A036464, A047659, A061994, A108792, A176186, A178721, A252593.

Main diagonal gives A000170.

Row sums give A287227.

T(2n,n) gives A348130.

Cf. A090642, A144084, A178717.