A334708 - OEIS

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.

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

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OFFSET

1,11

COMMENTS

Computed by Tom Duff, Jun 15 2020

LINKS

Table of n, a(n) for n=1..66.

Tom Duff, Data for tables A334708, A334709, A334710, A334711 for grids of size up to 192 X 192

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

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

Adjacent sequences: A334705 A334706 A334707 * A334709 A334710 A334711

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jun 15 2020.

STATUS

approved