A235454 Number of non-equivalent (mod D_4) ways to arrange 3 points on an n X n square grid so that they are not collinear.

1, 13, 70, 290, 867, 2266, 5068, 10475, 19764, 35406, 59817, 97375, 152154

Offset: 2

Author

Heinrich Ludwig, Jan 12 2014

Keywords

• nonn
• more

Comments

Column 3 of A235453.

Also number of non-equivalent triangles in an n X n grid.

Without the restriction "non-equivalent (mod D_4)" the numbers are given by A045996, n >= 2.

Examples

			There are a(3) = 13 non-equivalent ways to place 3 points on a 3 X 3 grid:
  . . .   . . .   X . .   . X .   . . .   . X .   . X .
  X . .   X . .   . . .   . . .   . X .   X . X   X X .
  X X .   X . X   X . X   X . X   X . X   . . .   . . .
-
  . . .   . . .   . . .   . X .   . X .   . . X
  X . X   . X X   X X .   . . X   X . .   X . .
  X . .   X . .   X . .   X . .   X . .   X . .
		

Crossrefs

Cf. A235453, A045996, A235455 (4 points), A235456 (5 points), A235457 (6 points), A235458 (7 points).

Extensions

a(13), a(14) from Heinrich Ludwig, Nov 16 2016