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

1,2

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.

Links

Table of n, a(n) for n=1..68.

Eric Weisstein's World of Mathematics, Visible Point

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A062069 A163375 A027011 * A267048 A350502 A326401

Adjacent sequences: A339397 A339398 A339399 * A339401 A339402 A339403

Keyword

nonn

Author

Torlach Rush, Dec 02 2020

Status

approved