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%I #8 Dec 09 2017 19:45:35
%S 0,0,0,0,17,4130,246498,6833514,114889560,1350364581,12098859685,
%T 87508246816,531900780705,2798253712804,13029075803653,54632738218122,
%U 209171316078609,739462342785714,2436048010628520,7535911103201627
%N Number of ways to arrange 12 points on an n X n X n triangular grid so that it balances at its center.
%C Column 12 of A194016.
%H R. H. Hardin, <a href="/A194015/b194015.txt">Table of n, a(n) for n = 1..27</a>
%e Some solutions for 7 X 7 X 7:
%e ........1..............1..............1..............1..............1
%e .......0.0............0.1............0.1............1.0............0.1
%e ......1.1.1..........0.1.1..........1.0.0..........0.0.0..........0.0.0
%e .....0.0.0.0........0.0.0.0........0.0.1.0........1.0.1.0........1.1.0.0
%e ....0.0.1.0.0......1.0.0.0.0......1.0.0.0.1......1.0.1.1.0......0.1.1.0.0
%e ...1.1.0.1.1.0....0.0.1.1.0.1....0.0.0.1.0.1....1.0.0.0.0.0....1.0.1.0.1.0
%e ..0.0.1.1.0.0.1..0.1.1.1.1.0.0..1.1.1.0.0.0.1..0.0.1.0.1.1.1..0.0.0.1.1.0.1
%K nonn
%O 1,5
%A _R. H. Hardin_, Aug 11 2011