A320540 (1/4) * number of ways to select 3 distinct collinear points from a square of grid points with side length n.

0, 2, 11, 38, 93, 206, 386, 678, 1112, 1748, 2583, 3768, 5253, 7172, 9630, 12720, 16370, 20910, 26169, 32566, 40139, 48962, 58900, 70710, 84096, 99284, 116469, 136116, 157671, 182436, 209436, 239596, 272976, 309630, 350035, 395346, 444021, 496890, 554402, 617906

Offset: 1

Author

Hugo Pfoertner, Oct 15 2018

Keywords

• nonn

Comments

Permutations of the 3 points are not counted separately.

Examples

			a(2) = 2 because there are 8 triples of collinear points in the square [0 2] X [0 2]: The 2*3 lines of x=0,1,2 and y=0,1,2 and the 2 diagonals.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..100

Crossrefs

(1/2)* diagonal of triangle A320539.

Cf. A115004, A320544.

Extensions

a(27)-a(40) from Giovanni Resta, Oct 26 2018