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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.

%I A320544 #11 Oct 26 2018 09:01:35
%S A320544 0,4,18,53,119,234,413,681,1047,1562,2243,3101,4186,5576,7231,9243,
%T A320544 11652,14518,17886,21779,26191,31368,37285,43919,51364,59894,69338,
%U A320544 79831,91495,104336,118513,134135,151072,169878,190229,212185,236040,262244,290317,320487
%N 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.
%C A320544 Permutations of the 3 points are not counted separately.
%H A320544 Giovanni Resta, <a href="/A320544/b320544.txt">Table of n, a(n) for n = 1..100</a>
%e A320544 a(1) = 0 because no triangle of area 1 can be formed from the corner points of the [0,1]X[0,1] square.
%e A320544 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.
%Y A320544 Diagonal of A320543.
%Y A320544 Cf. A115004, A320540.
%K A320544 nonn
%O A320544 1,2
%A A320544 _Hugo Pfoertner_, Oct 21 2018
%E A320544 a(27)-a(40) from _Giovanni Resta_, Oct 26 2018