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.
0, 0, 0, 39, 909, 8568, 50526, 221508, 789453, 2412333, 6542316, 16127397, 36762726, 78495417, 158548572, 305303544, 563965038, 1004432454, 1732013856, 2901747051, 4737236427, 7555075374, 11796103242, 18064943820, 27179490195, 40232239515
Offset: 1
Keywords
Examples
Some solutions for 4 X 4 X 4: .....0........0........0........0........0........1........1........0 ....0.1......0.1......1.0......1.0......1.0......0.0......1.0......0.1 ...1.1.0....1.0.1....1.0.1....0.1.1....1.0.1....1.0.1....0.1.0....1.0.1 ..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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..47
Crossrefs
Cf. A194480.
Formula
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.
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
Comments