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A334708
Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of ways to select four collinear points from an n X k grid.
8
0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 5, 2, 0, 2, 5, 15, 10, 3, 3, 10, 15, 35, 30, 15, 10, 15, 30, 35, 70, 70, 45, 29, 29, 45, 70, 70, 126, 140, 105, 72, 64, 72, 105, 140, 126, 210, 252, 210, 157, 129, 129, 157, 210, 252, 210, 330, 420, 378, 302, 248, 234, 248, 302, 378, 420, 330
OFFSET
1,11
COMMENTS
Computed by Tom Duff, Jun 15 2020
EXAMPLE
The initial rows of the array are:
0, 0, 0, 1, 5, 15, 35, 70, 126, 210, 330, 495, ...
0, 0, 0, 2, 10, 30, 70, 140, 252, 420, 660, 990, ...
0, 0, 0, 3, 15, 45, 105, 210, 378, 630, 990, 1485, ...
1, 2, 3, 10, 29, 72, 157, 302, 531, 874, 1361, 2028, ...
5, 10, 15, 29, 64, 129, 248, 442, 747, 1196, 1825, 2679, ...
15, 30, 45, 72, 129, 234, 405, 666, 1065, 1638, 2439, 3510, ...
35, 70, 105, 157, 248, 405, 660, 1020, 1545, 2276, 3283, 4605, ...
70, 140, 210, 302, 442, 666, 1020, 1524, 2220, 3154, 4412, 6030, ...
126, 252, 378, 531, 747, 1065, 1545, 2220, 3156, 4362, 5940, 7923, ...
210, 420, 630, 874, 1196, 1638, 2276, 3154, 4362, 5928, 7914, 10350, ...
...
The initial antidiagonals are:
0
0, 0
0, 0, 0
1, 0, 0, 1
5, 2, 0, 2, 5
15, 10, 3, 3, 10, 15
35, 30, 15, 10, 15, 30, 35
70, 70, 45, 29, 29, 45, 70, 70
126, 140, 105, 72, 64, 72, 105, 140, 126
210, 252, 210, 157, 129, 129, 157, 210, 252, 210
330, 420, 378, 302, 248, 234, 248, 302, 378, 420, 330
...
CROSSREFS
The main diagonal is A178256.
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: A375694 A244813 A078110 * A201528 A093814 A212155
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 15 2020.
STATUS
approved