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
Keywords
Examples
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
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.
Comments