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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)