%I #15 Aug 02 2017 23:40:56
%S 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,
%T 480,3028,9585,15108,10956,2910,231,2,1,49,960,9780,56520,190371,
%U 371016,404746,235380,68793,9030,252,0,1,64,1722,25574,231635,1336320,4988324
%N 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.
%C 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.
%C Rotations and reflections of a selection are regarded as different. If they are not to be counted, see A289229.
%H Heinrich Ludwig, <a href="/A289222/b289222.txt">Table of n, a(n) for n = 1..116, first 11 (and a half) rows of the triangular array</a>
%e The triangle begins:
%e 1;
%e 1, 1;
%e 1, 4, 0;
%e 1, 9, 12, 4;
%e 1, 16, 66, 82, 13, 0;
%e 1, 25, 204, 670, 859, 420, 76, 0;
%e 1, 36, 480, 3028, 9585, 15108, 10956, 2910, 231, 2;
%Y Cf. A289229, A289233.
%Y Columns 2 to 8: A000290, A289223, A289224, A289225, A289226, A289227, A289228.
%K tabf,nonn
%O 1,5
%A _Heinrich Ludwig_, Jul 03 2017