A194136 T(n,k) = number of ways to arrange k indistinguishable points on an n X n X n triangular grid so that no three points are collinear at any angle.

1, 0, 3, 0, 3, 6, 0, 1, 15, 10, 0, 0, 17, 45, 15, 0, 0, 6, 105, 105, 21, 0, 0, 0, 114, 407, 210, 28, 0, 0, 0, 39, 843, 1216, 378, 36, 0, 0, 0, 1, 792, 4122, 3036, 630, 45, 0, 0, 0, 0, 244, 7587, 14988, 6696, 990, 55, 0, 0, 0, 0, 9, 6480, 43836, 45414, 13428, 1485, 66, 0, 0, 0, 0

Offset: 1

Author

R. H. Hardin, Aug 17 2011

Keywords

• nonn
• tabl

Comments

Table starts

...1....0......0.......0.........0..........0...........0............0

...3....3......1.......0.........0..........0...........0............0

...6...15.....17.......6.........0..........0...........0............0

..10...45....105.....114........39..........1...........0............0

..15..105....407.....843.......792........244...........9............0

..21..210...1216....4122......7587.......6480........1875...........78

..28..378...3036...14988.....43836......69798.......52323........14268

..36..630...6696...45414....194013.....496198......695616.......464934

..45..990..13428..119340....696765....2595897.....5840088......7278867

..55.1485..25005..281442...2145687...10912452....35715529.....71089536

..66.2145..43861..608616...5851044...38739354...172520643....496946172

..78.3003..73277.1228812..14546412..121694240...708871152...2796515883

..91.4095.117471.2338779..33347130..342722071..2517687856..12966188538

.105.5460.181880.4240284..71662911..887407361..8023634766..52262929401

.120.7140.273268.7371414.145616964.2136513884.23292994812.187041426756

Examples

			Some solutions for n=4, k=4:
.....1........0........1........0........0........0........0........0
....0.0......1.1......1.0......0.1......1.1......1.0......1.1......0.1
...0.1.0....0.0.1....0.0.0....1.0.0....1.0.0....1.0.1....1.1.0....1.1.0
..1.0.0.1..1.0.0.0..0.1.1.0..0.1.0.1..0.0.1.0..0.0.1.0..0.0.0.0..0.0.0.1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..267
• S. V. Ullas Chandran, Sandi Klavžar, and James Tuite, The General Position Problem: A Survey, arXiv:2501.19385 [math.CO], 2025. See p. 4.

Crossrefs

Column 1 is A000217.

Column 2 is A050534.