A194482 Number of ways to arrange 5 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, 6, 234, 2817, 19362, 94584, 365904, 1193283, 3413619, 8800704, 20845968, 46017972, 95710797, 189154056, 357631176, 650438802, 1143119610, 1948614426, 3232108278, 5230489803, 8277505236, 12835867968, 19537783320, 29235566685

Offset

1,3

Comments

Column 5 of A194485.

Links

R. H. Hardin, Table of n, a(n) for n = 1..46

Formula

Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (1/384)*n^8 - (59/1920)*n^7 + (281/3840)*n^6 + (149/3840)*n^5 - (5/24)*n^4 + (29/320)*n^3 + (11/80)*n^2 - (1/10)*n.

Empirical g.f.: 3*x^3*(2 + 56*x + 191*x^2 + 85*x^3 - 31*x^4 + 11*x^5 + x^6) / (1 - x)^11. - Colin Barker, May 05 2018

Example

Some solutions for 4 X 4 X 4:
.....1........1........0........1........0........0........0........0
....1.1......1.0......1.1......0.0......0.1......1.1......1.0......1.1
...0.1.1....0.1.0....0.1.0....1.0.1....0.1.0....1.0.1....1.0.0....1.0.0
..0.0.0.0..0.1.0.1..0.1.1.0..1.1.0.0..0.1.1.1..0.1.0.0..1.1.0.1..1.1.0.0

Crossrefs

Cf. A194485.

Sequence in context: A221926 A324232 A307888 * A309330 A362733 A266657

Adjacent sequences: A194479 A194480 A194481 * A194483 A194484 A194485

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved