A194476 Number of ways to arrange 4 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, 6, 114, 879, 4284, 15729, 47565, 124803, 293733, 634293, 1277133, 2426424, 4389567, 7615062, 12739902, 20647962, 32540958, 50023656, 75205116, 110817861, 160356966, 228241167, 319998195, 442476645, 604086795, 815072895, 1087819551

Offset: 1

Author

R. H. Hardin, Aug 26 2011

Keywords

• nonn

Comments

Column 4 of A194480.

Examples

			All solutions for 3 X 3 X 3:
....0......1......0......1......1......0
...1.1....0.1....1.1....1.1....1.0....1.1
..0.1.1..1.1.0..1.1.0..0.1.0..0.1.1..1.0.1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..112

Crossrefs

Cf. A194480

Formula

Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (5/64)*n^6 + (13/240)*n^5 + (27/128)*n^4 - (23/96)*n^3 - (13/96)*n^2 + (7/40)*n.

Empirical g.f.: x^3*(2 + 20*x + 23*x^2 - 9*x^3 - x^4) / (1 - x)^9. - Colin Barker, May 05 2018