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

1,3

Comments

Column 4 of A194480.

Links

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

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

Example

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

Crossrefs

Cf. A194480

Sequence in context: A324669 A051228 A194132 * A059116 A121544 A274786

Adjacent sequences: A194473 A194474 A194475 * A194477 A194478 A194479

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved