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

Author

R. H. Hardin, Aug 18 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

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

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.