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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

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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.