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

1,3

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..267

Example

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

Crossrefs

Column 1 is A000217.

Column 2 is A050534.

Sequence in context: A014715 A131656 A194492 * A194480 A194485 A120987

Adjacent sequences: A194133 A194134 A194135 * A194137 A194138 A194139

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 17 2011

Status

approved