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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.
6
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
1,5
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.
EXAMPLE
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;
CROSSREFS
Columns 2 to 6: A001840, A117662, A289230, A289231, A289232.
Sequence in context: A370030 A124031 A368514 * A263097 A286011 A241954
KEYWORD
tabf,nonn
AUTHOR
Heinrich Ludwig, Jul 04 2017
STATUS
approved