A194481 Number of ways to arrange 4 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, 15, 207, 1347, 5922, 20307, 58527, 148239, 339669, 718344, 1422564, 2666664, 4771221, 8201466, 13615266, 21922146, 34354926, 52555653, 78677613, 115505313, 166594428, 236433813, 330631785, 456128985, 621440235, 836927910, 1115109450

Offset: 1

Author

R. H. Hardin, Aug 26 2011

Keywords

• nonn

Comments

Column 4 of A194485.

Examples

			Some solutions for 4 X 4 X 4:
.....0........0........1........0........0........0........0........0
....1.0......0.0......0.0......0.0......1.0......1.0......0.1......1.0
...1.1.1....1.0.1....1.0.1....1.0.1....1.0.0....1.0.0....0.0.1....1.0.1
..0.0.0.0..1.1.0.0..0.0.1.0..0.0.1.1..0.1.0.1..0.0.1.1..1.0.0.1..0.0.0.1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..84

Crossrefs

Cf. A194485.

Formula

Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (1/64)*n^6 - (13/120)*n^5 + (19/128)*n^4 + (7/96)*n^3 - (13/96)*n^2 + (1/40)*n.

Empirical g.f.: x^3*(5 + 24*x + 8*x^2 - 3*x^3 + x^4) / (1 - x)^9. - Colin Barker, May 05 2018