A194483 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.
0, 0, 1, 165, 4135, 47010, 337860, 1790472, 7622340, 27489825, 87018360, 247874770, 647091588, 1569661600, 3576049620, 7716906900, 15881735580, 31347485274, 59618165895, 109678780695, 195827638105, 340301983890, 576974687080
Offset: 1
Keywords
Examples
Some solutions for 5 X 5 X 5: ......0..........1..........0..........0..........0..........0..........0 .....0.1........1.0........0.1........0.1........0.1........1.0........1.0 ....0.1.0......0.1.1......0.0.1......1.0.1......0.1.0......0.1.0......0.1.1 ...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 ..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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..29
Formula
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
Comments