A194483 - OEIS

%I #8 Dec 09 2017 03:57:46

%S 0,0,1,165,4135,47010,337860,1790472,7622340,27489825,87018360,

%T 247874770,647091588,1569661600,3576049620,7716906900,15881735580,

%U 31347485274,59618165895,109678780695,195827638105,340301983890,576974687080

%N Number of ways to arrange 6 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 6 of A194485.

%H R. H. Hardin, <a href="/A194483/b194483.txt">Table of n, a(n) for n = 1..29</a>

%F Empirical: a(n) = (1/46080)*n^12 + (1/7680)*n^11 - (1/3072)*n^10 - (137/23040)*n^9 + (871/46080)*n^8 + (3107/161280)*n^7 - (5573/46080)*n^6 + (1157/23040)*n^5 + (2627/11520)*n^4 - (1121/5760)*n^3 - (181/1440)*n^2 + (11/84)*n

%e Some solutions for 5 X 5 X 5:

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

%e .....0.1........1.0........0.1........0.1........0.1........1.0........1.0

%e ....0.1.0......0.1.1......0.0.1......1.0.1......0.1.0......0.1.0......0.1.1

%e ...0.1.1.0....1.0.0.0....0.1.0.1....1.0.1.1....1.0.0.1....0.1.0.0....0.1.0.1

%e ..0.0.1.1.0..0.0.1.0.0..1.0.0.1.0..0.0.0.0.0..1.0.0.0.1..0.0.1.1.1..1.0.0.0.0

%K nonn

%O 1,4

%A _R. H. Hardin_, Aug 26 2011