A375480 For any n > 0, let L_n be the set of 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 L_{n-1} that are not is L_{n-2}.

0, 0, 1, 2, 1, 4, 2, 6, 3, 6, 7, 8, 8, 9, 7, 12, 9, 14, 12, 14, 15, 12, 15, 16, 8, 20, 17, 21, 23, 22, 18, 28, 25, 25, 31, 23, 33, 26, 29, 28, 39, 32, 30, 34, 29, 37, 41, 39, 43, 42, 31, 42, 33, 44, 38, 47, 50, 52, 39, 47, 49, 48, 44, 53, 61, 51, 59, 55, 56

Offset

1,4

Links

Table of n, a(n) for n=1..69.

Rémy Sigrist, PARI program

Example

The first terms, alongside the corresponding new lines, are:
  n  a(n)  Lines
  -  ----  --------------------------------------------------------
  1     0  {}
  2     0  {}
  3     1  {0}
  4     2  {1/2*x-1/2, x-2}
  5     1  {2/3*x-2/3}
  6     4  {1/4*x-1/4, 1/3*x-2/3, 1, -x+6}
  7     2  {4/5*x-4/5, 3*x-14}
  8     6  {1/3*x-1/3, 2/5*x-4/5, 1/4*x+1/4, 2, 1/2*x-3/2, -2*x+16}
  9     3  {6/7*x-6/7, 5/3*x-22/3, 4*x-26}

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A375479.

Sequence in context: A349442 A130742 A130107 * A107130 A194747 A065423

Adjacent sequences: A375477 A375478 A375479 * A375481 A375482 A375483

Keyword

nonn

Author

Rémy Sigrist, Aug 17 2024

Status

approved