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

1,2

Comments

Permutations of the 3 points are not counted separately.

Links

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

Example

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.

Crossrefs

Diagonal of A320543.

Cf. A115004, A320540.

Sequence in context: A301486 A284607 A297945 * A020644 A182031 A212250

Adjacent sequences: A320541 A320542 A320543 * A320545 A320546 A320547

Keyword

nonn

Author

Hugo Pfoertner, Oct 21 2018

Extensions

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

Status

approved