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%I #8 Dec 09 2017 03:57:02
%S 0,0,0,0,0,49,10010,413727,8363578,108576799,1030757941,7721414278,
%T 47957203600,255640086696,1199509369309,5050244459572,19366840027021,
%U 68459296434321,225242952960337,695338409837163,2027581798386055
%N Number of ways to arrange 12 points on an n X n X n triangular grid on an isosceles triangle so that it balances at the midpoint of its central altitude.
%C Column 12 of A194024.
%H R. H. Hardin, <a href="/A194023/b194023.txt">Table of n, a(n) for n = 1..31</a>
%e Some solutions for 6 X 6 X 6:
%e .......1............1............1............1............1............1
%e ......1.1..........1.1..........1.1..........1.1..........1.1..........1.1
%e .....1.1.1........1.1.1........1.1.1........1.1.1........1.0.1........1.1.1
%e ....1.0.1.1......1.1.0.1......0.1.1.1......1.0.1.1......1.1.1.1......1.0.1.1
%e ...0.1.0.1.0....1.0.1.0.0....1.0.0.0.1....0.0.1.1.0....0.1.1.1.0....1.0.1.0.0
%e ..0.0.1.0.0.0..0.0.0.0.0.1..0.1.0.0.0.0..0.1.0.0.0.0..0.0.0.0.0.0..0.0.0.0.1.0
%K nonn
%O 1,6
%A _R. H. Hardin_, Aug 12 2011
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