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%I #7 Dec 09 2017 03:57:51
%S 0,0,0,63,4080,83745,927471,6924357,39196161,180512640,708150465,
%T 2442836682,7582054194,21540941994,56763356130,140189208510,
%U 327211061058,726712057836,1544399756262,3155463833625,6223010262480,11886291766899
%N Number of ways to arrange 7 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 7 of A194485.
%F Empirical: a(n) = (1/645120)*n^14 + (1/92160)*n^13 - (1/30720)*n^12 - (79/92160)*n^11 + (101/30720)*n^10 + (757/129024)*n^9 - (3049/92160)*n^8 - (34099/645120)*n^7 + (6613/15360)*n^6 - (16859/23040)*n^5 + (1043/3840)*n^4 + (2759/5040)*n^3 - (753/1120)*n^2 + (13/56)*n.
%e Some solutions for 5 X 5 X 5:
%e ......1..........0..........0..........1..........0..........0..........0
%e .....0.1........1.0........1.1........0.1........1.1........0.1........0.0
%e ....1.1.1......0.1.0......1.1.1......1.0.0......0.0.0......0.1.1......1.0.1
%e ...0.0.0.0....1.1.0.0....1.0.1.0....1.0.1.0....1.1.0.1....0.1.1.0....1.1.0.1
%e ..1.1.0.0.0..0.1.0.1.1..0.0.0.0.0..0.1.0.0.1..0.1.0.1.0..1.0.0.0.1..1.0.0.1.0
%K nonn
%O 1,4
%A _R. H. Hardin_, Aug 26 2011
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