A194193 Square array read by antidiagonals downwards: T(n,k) = number of ways to arrange k indistinguishable points on an n X n square grid so that no three points are collinear at any angle.

1, 0, 4, 0, 6, 9, 0, 4, 36, 16, 0, 1, 76, 120, 25, 0, 0, 78, 516, 300, 36, 0, 0, 28, 1278, 2148, 630, 49, 0, 0, 2, 1668, 9498, 6768, 1176, 64, 0, 0, 0, 998, 25052, 47331, 17600, 2016, 81, 0, 0, 0, 204, 36698, 215448, 175952, 40120, 3240, 100, 0, 0, 0, 11, 26700, 620210

Offset

1,3

Comments

Columns 4..7 are A175383, A194190, A194191, A194192 respectively. - Heinrich Ludwig, Nov 16 2016

Links

R. H. Hardin and Heinrich Ludwig, Table of n, a(n) for n = 1..199, (first 181 terms from R. H. Hardin)

Example

Table starts:
...1.....0.......0........0..........0...........0............0............0
...4.....6.......4........1..........0...........0............0............0
...9....36......76.......78.........28...........2............0............0
..16...120.....516.....1278.......1668.........998..........204...........11
..25...300....2148.....9498......25052.......36698........26700.........8242
..36...630....6768....47331.....215448......620210......1073076......1035097
..49..1176...17600...175952....1189868.....5367308.....15657764.....28228158
..64..2016...40120...545764....5199888....34678364....159413700....491910848
..81..3240...82608..1461672...18520572...169259212...1108580092...5122725512
.100..4950..157252..3507553...56978440...682686652...6030207624..38914424892
.121..7260..280988..7701638..155627304..2356999994..26852315940.229093733030
.144.10296..477012.15773526..388897892..7294368210.104865006648
.169.14196..775172.30375194..894254904.20227526910
.196.19110.1214768.55695587.1932504496
.225.25200.1844512.97777392
.256.32640.2725000
...
Some solutions for n=4, k=4:
..0..0..1..0....0..0..0..0....0..0..0..0....0..0..1..0....1..0..0..0
..1..0..0..0....1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..1
..0..0..0..0....0..1..0..1....1..0..1..0....1..0..0..0....0..0..0..1
..0..0..1..1....0..1..0..0....0..1..0..0....0..0..0..1....1..0..0..0

Crossrefs

Column 1 is A000290.

Column 2 is A083374.

Column 3 is A045996.

Column 4 is A175383.

Column 5 is A194190.

Column 6 is A194191.

Column 7 is A194192.

Sequence in context: A361621 A354491 A262246 * A265644 A296230 A222889

Adjacent sequences: A194190 A194191 A194192 * A194194 A194195 A194196

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 18 2011

Status

approved