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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.

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