A018817 -id:A018817 - cp's OEIS frontend

A119437 Table T(n,k) = number of lines through exactly k points of an n X n grid of points.

6, 12, 8, 48, 4, 10, 108, 16, 4, 12, 248, 36, 4, 4, 14, 428, 64, 20, 4, 4, 16, 764, 100, 44, 4, 4, 4, 18, 1196, 204, 36, 24, 4, 4, 4, 20, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 2668, 396, 124, 40, 28, 4, 4, 4, 4, 24, 3824, 572, 200, 20, 60, 4, 4, 4, 4, 4, 26, 5244, 780, 236, 76, 44, 32

Offset: 2

Franklin T. Adams-Watters, May 19 2006

			From _Seiichi Manyama_, Nov 26 2017: (Start)
The table starts:
  n\k|   2    3   4   5   6   7   8
  ---+------------------------------
   2 |   6;
   3 |  12,   8;
   4 |  48,   4, 10;
   5 | 108   16,  4, 12;
   6 | 248,  36,  4,  4, 14;
   7 | 428,  64, 20,  4,  4, 16;
   8 | 764, 100, 44,  4,  4,  4, 18; (End)

Seiichi Manyama, Rows n = 2..141, flattened
S. Mustonen, On lines and their intersection points in a rectangular grid of points [From _Seppo Mustonen_, Apr 18 2009]
Seppo Mustonen, On lines and their intersection points in a rectangular grid of points [Local copy]

Row sums A018808; columns A018809-A018817. See A119439 for another version.

T(n,k) = 1/2 (f(n, k+1) - 2 f(n, k) + f(n, k-1)) where f(n, k) = Sum_{-n < kx < n, -n < ky < n, gcd(x, y)=1} (n - |kx|)*(n - |ky|). [Seppo Mustonen, Apr 18 2009]

An incorrect formula removed by Seppo Mustonen, Apr 25 2009

A119439 Triangle T(n,k) = number of sets of m points determined by the intersection of a line with an n X n grid of points.

Original entry on oeis.org

1, 1, 1, 1, 4, 6, 1, 9, 12, 8, 1, 16, 48, 4, 10, 1, 25, 108, 16, 4, 12, 1, 36, 248, 36, 4, 4, 14, 1, 49, 428, 64, 20, 4, 4, 16, 1, 64, 764, 100, 44, 4, 4, 4, 18, 1, 81, 1196, 204, 36, 24, 4, 4, 4, 20, 1, 100, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 1, 121, 2668, 396, 124, 40, 28, 4, 4, 4, 4

Offset: 0

Franklin T. Adams-Watters, May 19 2006

Each singleton point is determined by all but finitely many of the family of lines passing through that point and the empty set is determined by any randomly positioned line.

			The table starts:
1,
1,1,
1,4,6,
1,9,12,8,
1,16,48,4,10,

Row sums A119438; columns A000290, A018809-A018817. See A119437 for another version.

T(n,0) = 1, T(n,1) = n^2, T(n,k) = A119437(n,k) for k>1.

cp's OEIS Frontend

A119437 Table T(n,k) = number of lines through exactly k points of an n X n grid of points.

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