A375479 For any n > 0, let S_n be the set of slopes of the straight lines passing through the points (i, a(i)) and (j, a(j)) for i < j <= n; a(1) = a(2) = 0, and then a(n) is the number of elements in S_{n-1} that are not is S_{n-2}.

0, 0, 1, 2, 1, 3, 3, 0, 5, 3, 6, 3, 5, 2, 8, 8, 5, 5, 4, 8, 7, 3, 12, 14, 11, 4, 14, 12, 5, 11, 7, 11, 9, 7, 14, 7, 11, 7, 14, 9, 8, 13, 7, 11, 8, 9, 10, 4, 21, 23, 19, 15, 9, 14, 9, 14, 13, 13, 12, 9, 15, 8, 13, 10, 17, 13, 12, 8, 18, 14, 11, 12, 10, 17, 6

Offset

1,4

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Example

The first terms, alongside the corresponding slopes, are:
  n   a(n)  Slopes
  --  ----  -----------------------------------------------
   1     0  {}
   2     0  {}
   3     1  {0}
   4     2  {1/2, 1}
   5     1  {2/3}
   6     3  {-1, 1/4, 1/3}
   7     3  {3/5, 3/4, 2}
   8     0  {}
   9     5  {-3, -3/2, -1/2, -1/3, -1/5}
  10     3  {5/8, 5/7, 5}
  11     6  {-2, 1/6, 2/7, 3/8, 2/5, 3/2}
  12     3  {4/7, 5/6, 3}
  13     5  {-2/3, 1/8, 2/9, 3/11, 3/10}
  14     2  {5/12, 5/11}
  15     8  {-4/3, -3/5, -1/4, -1/7, -1/8, 1/11, 1/9, 2/13}

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A375480.

Sequence in context: A144243 A125210 A098434 * A212634 A162883 A081446

Adjacent sequences: A375476 A375477 A375478 * A375480 A375481 A375482

Keyword

nonn

Author

Rémy Sigrist, Aug 17 2024

Status

approved