A283113 Triangle read by rows: T(n,k) is the number of nonequivalent ways (mod D_3) to place k points on an n X n X n triangular grid so that no two of them are on the same row, column or diagonal (n >= 1).

1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 9, 5, 1, 5, 19, 23, 3, 1, 7, 38, 82, 40, 1, 1, 8, 66, 230, 242, 45, 1, 10, 110, 560, 1038, 533, 29, 1, 12, 170, 1208, 3504, 3546, 821, 6, 1, 14, 255, 2392, 9998, 16917, 9137, 807, 1, 16, 365, 4405, 25158, 64345, 63755, 17408, 422

Offset: 1

Author

Heinrich Ludwig, Mar 10 2017

Keywords

• nonn
• tabf

Comments

Length of n-th row is A004396(n) + 1, for 1 <= n <= 21, where A004396(n) is the maximal number of points that can be placed under the condition mentioned above.

Rotations and reflections of placements are not counted. If they are to be counted, see A193986.

In terms or triangular chess: Number of nonequivalent ways (mod D_3) to arrange k nonattacking rooks on an n X n X n board, k>=0, n>=1.

Examples

			The table begins with T(1,0), T(1,1);
  1,  1;
  1,  1;
  1,  2,   1;
  1,  3,   3,   1;
  1,  4,   9,   5;
  1,  5,  19,  23,    3;
  1,  7,  38,  82,   40,   1;
  1,  8,  66, 230,  242,  45;
  1, 10, 110, 560, 1038, 533, 29;
  ...
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 1..175

Crossrefs

Row sums give A283117.

Columns 2..6: A001399, A005994, A283114, A283115, A283116.

Cf. A004396, A193986.