A320544 (1/8) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1 from a square of grid points with side length n.

0, 4, 18, 53, 119, 234, 413, 681, 1047, 1562, 2243, 3101, 4186, 5576, 7231, 9243, 11652, 14518, 17886, 21779, 26191, 31368, 37285, 43919, 51364, 59894, 69338, 79831, 91495, 104336, 118513, 134135, 151072, 169878, 190229, 212185, 236040, 262244, 290317, 320487

Offset: 1

Author

Hugo Pfoertner, Oct 21 2018

Keywords

• nonn

Comments

Permutations of the 3 points are not counted separately.

Examples

			a(1) = 0 because no triangle of area 1 can be formed from the corner points of the [0,1]X[0,1] square.
a(2) = 4 because 3 triangles of area 1 can be formed by connecting the end points of any of the 8 segments of length 1 on the periphery of the [0,2]X[0,2] square to any of the 3 vertices on the opposite side of the grid square, making 8*3 = 24 triangles. Additionally, 4 triangles of the type (0,0),(0,2),(1,2) and another 4 triangles of the type (2,1),(0,1),(1,0) can be selected. 24 + 4 + 4 = 32, a(2) = 32/8 = 4.
		

Links

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

Crossrefs

Diagonal of A320543.

Cf. A115004, A320540.

Extensions

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