This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279445 #14 Dec 23 2016 21:44:18 %S A279445 1,1,1,4,6,4,1,1,9,36,78,90,45,6,1,16,120,528,1428,2304,2040,816,90,1, %T A279445 25,300,2200,10600,34020,71400,93000,67950,22650,2040,1,36,630,6900, %U A279445 51525,270720,1005720,2602800,4531950,4987800,3110940,888840,67950,1,49,1176,17934 %N A279445 Triangle read by rows: T(n, k) is the number of ways to place k points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line. %C A279445 Length of n-th row is A272651(n) + 1, where A272651(n) is the maximal number of points to be placed under the condition mentioned. %C A279445 Rotations and reflections of placements are counted. If they are to be ignored, see A279453. %C A279445 For condition "no more than 2 points on a straight line at any angle", see A194193 (but that one is read by antidiagonals). %H A279445 Heinrich Ludwig, <a href="/A279445/b279445.txt">Table of n, a(n) for n = 1..109</a> %e A279445 The table begins with T(1, 0): %e A279445 1 1 %e A279445 1 4 6 4 1 %e A279445 1 9 36 78 90 45 6 %e A279445 1 16 120 528 1428 2304 2040 816 90 %e A279445 1 25 300 2200 10600 34020 71400 93000 67950 22650 2040 %e A279445 ... %e A279445 T(3, 2) = 36 because there are 36 ways to place 2 points on a 3 X 3 square grid so that no more than 2 points are on a vertical or horizontal straight line. %Y A279445 Row sums give A197458. %Y A279445 Columns 2..10: A000290, A083374, A279437, A279438, A279439, A279440, A279441, A279442, A279443. %Y A279445 Diagonal T(n, n) is A279444. %Y A279445 Cf. A279453, A194193. %K A279445 nonn,tabf %O A279445 1,4 %A A279445 _Heinrich Ludwig_, Dec 17 2016