A194482 - OEIS

%I #12 May 05 2018 08:07:06

%S 0,0,6,234,2817,19362,94584,365904,1193283,3413619,8800704,20845968,

%T 46017972,95710797,189154056,357631176,650438802,1143119610,

%U 1948614426,3232108278,5230489803,8277505236,12835867968,19537783320,29235566685

%N Number of ways to arrange 5 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 5 of A194485.

%H R. H. Hardin, <a href="/A194482/b194482.txt">Table of n, a(n) for n = 1..46</a>

%F Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (1/384)*n^8 - (59/1920)*n^7 + (281/3840)*n^6 + (149/3840)*n^5 - (5/24)*n^4 + (29/320)*n^3 + (11/80)*n^2 - (1/10)*n.

%F Empirical g.f.: 3*x^3*(2 + 56*x + 191*x^2 + 85*x^3 - 31*x^4 + 11*x^5 + x^6) / (1 - x)^11. - _Colin Barker_, May 05 2018

%e Some solutions for 4 X 4 X 4:

%e .....1........1........0........1........0........0........0........0

%e ....1.1......1.0......1.1......0.0......0.1......1.1......1.0......1.1

%e ...0.1.1....0.1.0....0.1.0....1.0.1....0.1.0....1.0.1....1.0.0....1.0.0

%e ..0.0.0.0..0.1.0.1..0.1.1.0..1.1.0.0..0.1.1.1..0.1.0.0..1.1.0.1..1.1.0.0

%Y Cf. A194485.

%K nonn

%O 1,3

%A _R. H. Hardin_, Aug 26 2011