A279453 - OEIS

%I #9 Dec 17 2016 10:58:24

%S 1,1,1,1,2,1,1,1,3,8,14,17,9,2,1,3,21,73,202,306,285,115,20,1,6,49,

%T 301,1397,4361,9110,11810,8679,2929,288,1,6,93,890,6582,34059,126396,

%U 326190,568134,624875,390426,111798,8791,1,10,171,2321,24185,185181,1055025

%N Triangle read by rows: T(n, k) is the number of nonequivalent 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 Length of n-th row is A272651(n) + 1, where A272651(n) is the maximal number of points that can be placed under the condition mentioned.

%C Rotations and reflections of placements are not counted. If they are to be counted, see A279445.

%C For condition "no more than 2 points on a straight line at any angle", see A235453.

%H Heinrich Ludwig, <a href="/A279453/b279453.txt">Table of n, a(n) for n = 1..109</a>

%e The table begins with T(1, 0):

%e 1 1

%e 1 1  2   1    1

%e 1 3  8  14   17    9    2

%e 1 3 21  73  202  306  285   115   20

%e 1 6 49 301 1397 4361 9110 11810 8679 2929 288

%e ...

%e T(4, 3) = 73 because there are 73 nonequivalent ways to place 3 points on a 4 X 4 square grid so that no more than 2 points are on a vertical or horizontal straight line.

%Y Row sums give A279454.

%Y Columns 2..8: A008805, A014409, A279454, A279455, A279456, A279457, A279458.

%Y Diagonal T(n, n) is A279452.

%Y Cf. A279445, A235453.

%K nonn,tabf

%O 1,5

%A _Heinrich Ludwig_, Dec 17 2016