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A334709
Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of ways to select four points from an n X k grid so that three of them form a triangle of nonzero area and the extra point is strictly inside the triangle.
7
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 48, 48, 0, 0, 0, 0, 144, 240, 144, 0, 0, 0, 0, 348, 716, 716, 348, 0, 0, 0, 0, 700, 1712, 2100, 1712, 700, 0, 0, 0, 0, 1280, 3404, 4984, 4984, 3404, 1280, 0, 0, 0, 0, 2144, 6176, 9900, 11604, 9900, 6176, 2144, 0, 0, 0, 0, 3400, 10336, 17936, 22936, 22936, 17936, 10336, 3400, 0, 0
OFFSET
1,13
COMMENTS
Computed by Tom Duff, Jun 15 2020
EXAMPLE
The initial rows of the array are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 8, 48, 144, 348, 700, 1280, 2144, 3400, 5120, 7440, ...
0, 0, 48, 240, 716, 1712, 3404, 6176, 10336, 16288, 24480, 35504, ...
0, 0, 144, 716, 2100, 4984, 9900, 17936, 29924, 47080, 70700, 102460, ...
0, 0, 348, 1712, 4984, 11604, 22936, 41372, 68844, 108132, 161964, 234228, ...
0, 0, 700, 3404, 9900, 22936, 45184, 81320, 135192, 212152, 317492, 458812, ...
0, 0, 1280, 6176, 17936, 41372, 81320, 145648, 241544, 378400, 565636, 816520, ...
0, 0, 2144, 10336, 29924, 68844, 135192, 241544, 399656, 625232, 933808, 1346928, ...
0, 0, 3400, 16288, 47080, 108132, 212152, 378400, 625232, 976552, 1457172, 2100112, ...
...
The initial antidiagonals are:
0,
0, 0,
0, 0, 0,
0, 0, 0, 0,
0, 0, 8, 0, 0,
0, 0, 48, 48, 0, 0,
0, 0, 144, 240, 144, 0, 0,
0, 0, 348, 716, 716, 348, 0, 0,
0, 0, 700, 1712, 2100, 1712, 700, 0, 0,
0, 0, 1280, 3404, 4984, 4984, 3404, 1280, 0, 0,
0, 0, 2144, 6176, 9900, 11604, 9900, 6176, 2144, 0, 0,
0, 0, 3400, 10336, 17936, 22936, 22936, 17936, 10336, 3400, 0, 0,
...
CROSSREFS
The main diagonal is A334712.
Triangles A334708, A334709, A334710, A334711 give the counts for the four possible arrangements of four points.
For three points there are just two possible arrangements: see A334704 and A334705.
Sequence in context: A374087 A325737 A272625 * A220667 A317445 A199619
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 15 2020
STATUS
approved