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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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 regarded as different. If they are not to be counted, see A289229.

LINKS

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

EXAMPLE

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;

CROSSREFS

Cf. A289229, A289233.

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

Sequence in context: A199786 A189245 A342372 * A121301 A059056 A344393

Adjacent sequences:  A289219 A289220 A289221 * A289223 A289224 A289225

KEYWORD

tabf,nonn

AUTHOR

Heinrich Ludwig, Jul 03 2017

STATUS

approved

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Last modified September 17 15:51 EDT 2021. Contains 347478 sequences. (Running on oeis4.)