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%I #13 May 05 2018 08:06:54
%S 0,0,15,207,1347,5922,20307,58527,148239,339669,718344,1422564,
%T 2666664,4771221,8201466,13615266,21922146,34354926,52555653,78677613,
%U 115505313,166594428,236433813,330631785,456128985,621440235,836927910,1115109450
%N Number of ways to arrange 4 indistinguishable points on an n X n X n triangular grid so that no four points are in the same row or diagonal.
%C Column 4 of A194485.
%H R. H. Hardin, <a href="/A194481/b194481.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (1/64)*n^6 - (13/120)*n^5 + (19/128)*n^4 + (7/96)*n^3 - (13/96)*n^2 + (1/40)*n.
%F Empirical g.f.: x^3*(5 + 24*x + 8*x^2 - 3*x^3 + x^4) / (1 - x)^9. - _Colin Barker_, May 05 2018
%e Some solutions for 4 X 4 X 4:
%e .....0........0........1........0........0........0........0........0
%e ....1.0......0.0......0.0......0.0......1.0......1.0......0.1......1.0
%e ...1.1.1....1.0.1....1.0.1....1.0.1....1.0.0....1.0.0....0.0.1....1.0.1
%e ..0.0.0.0..1.1.0.0..0.0.1.0..0.0.1.1..0.1.0.1..0.0.1.1..1.0.0.1..0.0.0.1
%Y Cf. A194485.
%K nonn
%O 1,3
%A _R. H. Hardin_, Aug 26 2011
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