A279453 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.

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, 301, 1397, 4361, 9110, 11810, 8679, 2929, 288, 1, 6, 93, 890, 6582, 34059, 126396, 326190, 568134, 624875, 390426, 111798, 8791, 1, 10, 171, 2321, 24185, 185181, 1055025

Offset: 1

Author

Heinrich Ludwig, Dec 17 2016

Keywords

• nonn
• tabf

Comments

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.

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

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

Examples

			The table begins with T(1, 0):
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 49 301 1397 4361 9110 11810 8679 2929 288
...
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.
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 1..109

Crossrefs

Row sums give A279454.

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

Diagonal T(n, n) is A279452.

Cf. A279445, A235453.