A289229 Triangle read by rows: T(n, k) is the number of nonequivalent 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, 2, 0, 1, 3, 3, 2, 1, 5, 14, 19, 4, 0, 1, 7, 40, 127, 159, 77, 17, 0, 1, 9, 90, 536, 1644, 2569, 1876, 500, 42, 1, 1, 12, 175, 1688, 9548, 31951, 62171, 67765, 39459, 11579, 1547, 47, 0, 1, 15, 308, 4357, 38872, 223346, 832628, 2005948, 3072004, 2897626

Offset: 1

Author

Heinrich Ludwig, Jul 04 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 not counted. If they are to be counted, see A289222.

Examples

			The triangle begins:
  1;
  1,  1;
  1,  2,   0;
  1,  3,   3,    3;
  1,  5,  14,   19,    4,     0;
  1,  7,  40,  127,  159,    77,    17,     0;
  1,  9,  90,  536, 1644,  2569,  1876,   500,    42,     1;
  1, 12, 175, 1688, 9548, 31951, 62171, 67765, 39459, 11579, 1547, 47, 0;
		

Links

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

Crossrefs

Cf. A289222, A289233.

Columns 2 to 6: A001840, A117662, A289230, A289231, A289232.