A289222 Triangle read by rows: T(n, k) is the number of ways to select k disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.

1, 1, 1, 1, 4, 0, 1, 9, 12, 4, 1, 16, 66, 82, 13, 0, 1, 25, 204, 670, 859, 420, 76, 0, 1, 36, 480, 3028, 9585, 15108, 10956, 2910, 231, 2, 1, 49, 960, 9780, 56520, 190371, 371016, 404746, 235380, 68793, 9030, 252, 0, 1, 64, 1722, 25574, 231635, 1336320, 4988324

Offset: 1

Author

Heinrich Ludwig, Jul 03 2017

Keywords

• tabf
• nonn

Comments

The row index starts from 1. The column index k runs from 0 to floor(n*(n+1)/6), which is a trivial upper bound for the maximal number of 2 X 2 X 2 triangles that can be selected from an n X n X n triangular grid.

Rotations and reflections of a selection are regarded as different. If they are not to be counted, see A289229.

Examples

			The triangle begins:
  1;
  1,  1;
  1,  4,   0;
  1,  9,  12,    4;
  1, 16,  66,   82,   13,     0;
  1, 25, 204,  670,  859,   420,    76,    0;
  1, 36, 480, 3028, 9585, 15108, 10956, 2910, 231, 2;
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 1..116, first 11 (and a half) rows of the triangular array

Crossrefs

Cf. A289229, A289233.

Columns 2 to 8: A000290, A289223, A289224, A289225, A289226, A289227, A289228.