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A320539 (1/2) * number of ways to select 3 distinct collinear points from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k. 3
0, 1, 4, 4, 10, 22, 10, 21, 42, 76, 20, 39, 70, 120, 186, 35, 65, 112, 184, 279, 412, 56, 100, 166, 264, 390, 566, 772, 84, 146, 236, 367, 532, 759, 1026, 1356, 120, 205, 324, 494, 704, 991, 1326, 1740, 2224, 165, 278, 432, 647, 913, 1271, 1686, 2196, 2793, 3496 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Permutations of the 3 points are not counted separately.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

The triangle begins:

    0

    1    4

    4   10   22

   10   21   42   76

   20   39   70  120  186

   35   65  112  184  279  412

   56  100  166  264  390  566  772

.

a(2) = T(1,2) = 1, because the grid points on the two longer sides of the rectangle are collinear: (0,0) (0,1) (0,2) and (1,0) (1,1) (2,2).

a(3) = T(2,2) = 4, because there are 8 triples of collinear points:

  (0,0) (0,1) (0,2),

  (0,0) (1,0) (2,0),

  (0,0) (1,1) (2,2),

  (0,1) (1,1) (2,1),

  (0,2) (1,1) (2,0),

  (0,2) (1,2) (2,2),

  (1,0) (1,1) (1,2),

  (2,0) (2,1) (2,2).

CROSSREFS

A000292, A320540, A320541, A320543.

Sequence in context: A178820 A284784 A219803 * A145598 A320392 A117881

Adjacent sequences:  A320536 A320537 A320538 * A320540 A320541 A320542

KEYWORD

nonn,tabl

AUTHOR

Hugo Pfoertner, Oct 15 2018

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)