A194484 Number of ways to arrange 7 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, 0, 63, 4080, 83745, 927471, 6924357, 39196161, 180512640, 708150465, 2442836682, 7582054194, 21540941994, 56763356130, 140189208510, 327211061058, 726712057836, 1544399756262, 3155463833625, 6223010262480, 11886291766899

Offset

1,4

Comments

Column 7 of A194485.

Links

Table of n, a(n) for n=1..22.

Formula

Empirical: a(n) = (1/645120)*n^14 + (1/92160)*n^13 - (1/30720)*n^12 - (79/92160)*n^11 + (101/30720)*n^10 + (757/129024)*n^9 - (3049/92160)*n^8 - (34099/645120)*n^7 + (6613/15360)*n^6 - (16859/23040)*n^5 + (1043/3840)*n^4 + (2759/5040)*n^3 - (753/1120)*n^2 + (13/56)*n.

Example

Some solutions for 5 X 5 X 5:
......1..........0..........0..........1..........0..........0..........0
.....0.1........1.0........1.1........0.1........1.1........0.1........0.0
....1.1.1......0.1.0......1.1.1......1.0.0......0.0.0......0.1.1......1.0.1
...0.0.0.0....1.1.0.0....1.0.1.0....1.0.1.0....1.1.0.1....0.1.1.0....1.1.0.1
..1.1.0.0.0..0.1.0.1.1..0.0.0.0.0..0.1.0.0.1..0.1.0.1.0..1.0.0.0.1..1.0.0.1.0

Crossrefs

Sequence in context: A180926 A267963 A268028 * A195620 A238994 A364745

Adjacent sequences: A194481 A194482 A194483 * A194485 A194486 A194487

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved