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

1,2

Comments

Permutations of the 3 points are not counted separately.

Links

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

Example

a(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.

Crossrefs

(1/2)* diagonal of triangle A320539.

Cf. A115004, A320544.

Sequence in context: A038607 A079009 A097651 * A059673 A294152 A196701

Adjacent sequences: A320537 A320538 A320539 * A320541 A320542 A320543

Keyword

nonn

Author

Hugo Pfoertner, Oct 15 2018

Extensions

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

Status

approved