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

1,3

Comments

Column 4 of A194485.

Links

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

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

Example

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

Crossrefs

Cf. A194485.

Sequence in context: A231546 A362809 A063906 * A078265 A089138 A271333

Adjacent sequences: A194478 A194479 A194480 * A194482 A194483 A194484

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved