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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.

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%I A320540 #11 Oct 26 2018 09:27:09
%S A320540 0,2,11,38,93,206,386,678,1112,1748,2583,3768,5253,7172,9630,12720,
%T A320540 16370,20910,26169,32566,40139,48962,58900,70710,84096,99284,116469,
%U A320540 136116,157671,182436,209436,239596,272976,309630,350035,395346,444021,496890,554402,617906
%N A320540 (1/4) * number of ways to select 3 distinct collinear points from a square of grid points with side length n.
%C A320540 Permutations of the 3 points are not counted separately.
%H A320540 Giovanni Resta, <a href="/A320540/b320540.txt">Table of n, a(n) for n = 1..100</a>
%e A320540 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.
%Y A320540 (1/2)* diagonal of triangle A320539.
%Y A320540 Cf. A115004, A320544.
%K A320540 nonn
%O A320540 1,2
%A A320540 _Hugo Pfoertner_, Oct 15 2018
%E A320540 a(27)-a(40) from _Giovanni Resta_, Oct 26 2018