A194483 Number of ways to arrange 6 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, 1, 165, 4135, 47010, 337860, 1790472, 7622340, 27489825, 87018360, 247874770, 647091588, 1569661600, 3576049620, 7716906900, 15881735580, 31347485274, 59618165895, 109678780695, 195827638105, 340301983890, 576974687080

Offset

1,4

Comments

Column 6 of A194485.

Links

R. H. Hardin, Table of n, a(n) for n = 1..29

Formula

Empirical: a(n) = (1/46080)*n^12 + (1/7680)*n^11 - (1/3072)*n^10 - (137/23040)*n^9 + (871/46080)*n^8 + (3107/161280)*n^7 - (5573/46080)*n^6 + (1157/23040)*n^5 + (2627/11520)*n^4 - (1121/5760)*n^3 - (181/1440)*n^2 + (11/84)*n

Example

Some solutions for 5 X 5 X 5:
......0..........1..........0..........0..........0..........0..........0
.....0.1........1.0........0.1........0.1........0.1........1.0........1.0
....0.1.0......0.1.1......0.0.1......1.0.1......0.1.0......0.1.0......0.1.1
...0.1.1.0....1.0.0.0....0.1.0.1....1.0.1.1....1.0.0.1....0.1.0.0....0.1.0.1
..0.0.1.1.0..0.0.1.0.0..1.0.0.1.0..0.0.0.0.0..1.0.0.0.1..0.0.1.1.1..1.0.0.0.0

Crossrefs

Sequence in context: A184490 A027796 A145055 * A105944 A071576 A140912

Adjacent sequences: A194480 A194481 A194482 * A194484 A194485 A194486

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved