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A194477 Number of ways to arrange 5 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.

%I A194477 #12 May 05 2018 08:06:41
%S A194477 0,0,0,39,909,8568,50526,221508,789453,2412333,6542316,16127397,
%T A194477 36762726,78495417,158548572,305303544,563965038,1004432454,
%U A194477 1732013856,2901747051,4737236427,7555075374,11796103242,18064943820,27179490195,40232239515
%N A194477 Number of ways to arrange 5 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
%C A194477 Column 5 of A194480.
%H A194477 R. H. Hardin, <a href="/A194477/b194477.txt">Table of n, a(n) for n = 1..47</a>
%F A194477 Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (7/384)*n^8 + (37/1920)*n^7 + (737/3840)*n^6 - (2347/3840)*n^5 + (101/192)*n^4 + (93/320)*n^3 - (7/10)*n^2 + (3/10)*n.
%F A194477 Empirical g.f.: 3*x^4*(13 + 160*x + 238*x^2 - 54*x^3 - 51*x^4 + 9*x^5) / (1 - x)^11. - _Colin Barker_, May 05 2018
%e A194477 Some solutions for 4 X 4 X 4:
%e A194477 .....0........0........0........0........0........1........1........0
%e A194477 ....0.1......0.1......1.0......1.0......1.0......0.0......1.0......0.1
%e A194477 ...1.1.0....1.0.1....1.0.1....0.1.1....1.0.1....1.0.1....0.1.0....1.0.1
%e A194477 ..0.0.1.1..0.1.1.0..0.1.1.0..1.1.0.0..0.1.0.1..0.1.1.0..0.1.0.1..1.1.0.0
%Y A194477 Cf. A194480.
%K A194477 nonn
%O A194477 1,4
%A A194477 _R. H. Hardin_, Aug 26 2011