A339400 Mark each point on the n X n grid with the number of points that are visible from it; a(n) is the number of distinct values in the grid.

1, 3, 3, 4, 3, 7, 5, 7, 7, 11, 5, 14, 8, 13, 13, 19, 9, 22, 11, 23, 21, 25, 13, 29, 21, 34, 26, 37, 11, 40, 26, 44, 31, 45, 21, 54, 35, 54, 36, 55, 24, 65, 40, 59, 47, 70, 24, 71, 43, 72, 55, 81, 28, 74, 55, 88, 59, 90, 28, 93, 58, 91, 66, 96, 46, 110, 63, 100

Offset: 1

Author

Torlach Rush, Dec 02 2020

Keywords

• nonn

Comments

a(n) <= A008805(n). This is because A008805(n) is the maximum number of points required to calculate a(n) and each point is located in the first quadrant.

Examples

			a(1) = 1 because there are 3 visible points from every point on the grid.
a(2) = 3 because 5 points are visible from every vertex of the grid, 7 points are visible from the midpoint of every edge of the grid, and 8 points are visible from the middle of the grid.
a(3) = 3 because 9 points are visible from every vertex of the grid, 11 points are visible from the inner points of every edge of the grid, and 12 points are visible from every inner point of the grid.
		

Links

• Eric Weisstein's World of Mathematics, Visible Point

Crossrefs

Cf. A008805, A049687, A049691, A300778, A331771.

Programs

PARI

\\ n = side length, d = dimension
cdvps(n, d) ={my(m=Map());
  forvec(u=vector(d, i, [0, n\2]),
    my(c=0); forvec(v=[[t-n, t]|t<-u], c+=(gcd(v)==1));
    mapput(m, c, 1), 1);
  #m; }
a(n) = cdvps(n, 2)