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.

1, 1, 1, 4, 6, 4, 1, 1, 9, 36, 78, 90, 45, 6, 1, 16, 120, 528, 1428, 2304, 2040, 816, 90, 1, 25, 300, 2200, 10600, 34020, 71400, 93000, 67950, 22650, 2040, 1, 36, 630, 6900, 51525, 270720, 1005720, 2602800, 4531950, 4987800, 3110940, 888840, 67950, 1, 49, 1176, 17934

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 to be placed under the condition mentioned.

Rotations and reflections of placements are counted. If they are to be ignored, see A279453.

For condition "no more than 2 points on a straight line at any angle", see A194193 (but that one is read by antidiagonals).

Examples

			The table begins with T(1, 0):
1  1
1  4   6    4     1
1  9  36   78    90    45     6
1 16 120  528  1428  2304  2040   816    90
1 25 300 2200 10600 34020 71400 93000 67950 22650 2040
...
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.
		

Links

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

Crossrefs

Row sums give A197458.

Columns 2..10: A000290, A083374, A279437, A279438, A279439, A279440, A279441, A279442, A279443.

Diagonal T(n, n) is A279444.

Cf. A279453, A194193.