

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.


6



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
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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(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



