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

2,1

Links

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]

Formula

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]

Example

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)

Crossrefs

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

Sequence in context: A162522 A292680 A028320 * A243033 A242549 A315777

Adjacent sequences: A119434 A119435 A119436 * A119438 A119439 A119440

Keyword

nonn,tabl

Author

Franklin T. Adams-Watters, May 19 2006

Extensions

An incorrect formula removed by Seppo Mustonen, Apr 25 2009

Status

approved