cp's OEIS Frontend

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.

%I A194193 #24 Dec 09 2017 19:46:23
%S A194193 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,
%T A194193 2148,630,49,0,0,2,1668,9498,6768,1176,64,0,0,0,998,25052,47331,17600,
%U A194193 2016,81,0,0,0,204,36698,215448,175952,40120,3240,100,0,0,0,11,26700,620210
%N 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.
%C A194193 Columns 4..7 are A175383, A194190, A194191, A194192 respectively. - _Heinrich Ludwig_, Nov 16 2016
%H A194193 R. H. Hardin and Heinrich Ludwig, <a href="/A194193/b194193.txt">Table of n, a(n) for n = 1..199</a>, (first 181 terms from R. H. Hardin)
%e A194193 Table starts:
%e A194193 ...1.....0.......0........0..........0...........0............0............0
%e A194193 ...4.....6.......4........1..........0...........0............0............0
%e A194193 ...9....36......76.......78.........28...........2............0............0
%e A194193 ..16...120.....516.....1278.......1668.........998..........204...........11
%e A194193 ..25...300....2148.....9498......25052.......36698........26700.........8242
%e A194193 ..36...630....6768....47331.....215448......620210......1073076......1035097
%e A194193 ..49..1176...17600...175952....1189868.....5367308.....15657764.....28228158
%e A194193 ..64..2016...40120...545764....5199888....34678364....159413700....491910848
%e A194193 ..81..3240...82608..1461672...18520572...169259212...1108580092...5122725512
%e A194193 .100..4950..157252..3507553...56978440...682686652...6030207624..38914424892
%e A194193 .121..7260..280988..7701638..155627304..2356999994..26852315940.229093733030
%e A194193 .144.10296..477012.15773526..388897892..7294368210.104865006648
%e A194193 .169.14196..775172.30375194..894254904.20227526910
%e A194193 .196.19110.1214768.55695587.1932504496
%e A194193 .225.25200.1844512.97777392
%e A194193 .256.32640.2725000
%e A194193 ...
%e A194193 Some solutions for n=4, k=4:
%e A194193 ..0..0..1..0....0..0..0..0....0..0..0..0....0..0..1..0....1..0..0..0
%e A194193 ..1..0..0..0....1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..1
%e A194193 ..0..0..0..0....0..1..0..1....1..0..1..0....1..0..0..0....0..0..0..1
%e A194193 ..0..0..1..1....0..1..0..0....0..1..0..0....0..0..0..1....1..0..0..0
%Y A194193 Column 1 is A000290.
%Y A194193 Column 2 is A083374.
%Y A194193 Column 3 is A045996.
%Y A194193 Column 4 is A175383.
%Y A194193 Column 5 is A194190.
%Y A194193 Column 6 is A194191.
%Y A194193 Column 7 is A194192.
%K A194193 nonn,tabl
%O A194193 1,3
%A A194193 _R. H. Hardin_, Aug 18 2011