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%I #9 Dec 09 2017 19:45:23
%S 0,0,1,12,136,909,4350,16602,53679,152553,391425,923809,2033619,
%T 4220293,8326008,15719472,28556469,50138721,85400418,141555750,
%U 228947893,362144832,561340717,854121696,1277672814,1881508263,2730820641
%N Number of ways to arrange 6 points on an n X n X n triangular grid so that it balances at its center.
%C Column 6 of A194016.
%H R. H. Hardin, <a href="/A194013/b194013.txt">Table of n, a(n) for n = 1..57</a>
%e Some solutions for 7 X 7 X 7:
%e ........0..............0..............0..............1..............0
%e .......0.0............0.0............0.0............0.0............1.0
%e ......1.1.0..........0.1.1..........0.1.0..........0.0.0..........0.0.0
%e .....0.0.1.0........0.0.0.0........1.1.0.0........1.1.0.0........0.0.1.0
%e ....0.0.0.0.0......0.0.0.0.1......0.0.0.0.1......0.0.0.0.0......0.0.0.1.0
%e ...0.0.0.1.0.0....1.0.0.0.1.0....0.0.0.0.0.0....0.0.0.0.0.0....1.0.0.0.1.0
%e ..0.0.1.0.1.0.0..0.1.0.0.0.0.0..0.1.0.0.0.1.0..1.0.0.0.0.1.1..0.0.0.1.0.0.0
%K nonn
%O 1,4
%A _R. H. Hardin_, Aug 11 2011
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