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

1,4

Comments

Column 5 of A194480.

Links

R. H. Hardin, Table of n, a(n) for n = 1..47

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

Example

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

Crossrefs

Cf. A194480.

Sequence in context: A264458 A004330 A069418 * A016091 A028227 A028219

Adjacent sequences: A194474 A194475 A194476 * A194478 A194479 A194480

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved