A339947 Mark each point on the n X n X 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, 5, 5, 13, 5, 33, 23, 30, 25, 69, 23, 150, 79, 119, 161, 385, 125, 501, 178, 443, 548, 1105, 273, 1119, 921, 1339, 1202, 2049, 228, 2237, 2041, 2792, 2431, 3096, 1006, 5905, 4216, 5230, 3433, 7596, 1531, 10026, 6556, 6939, 8201, 14190, 3105, 13431, 7068, 12673, 12587, 22075, 4080, 17211, 13183, 19462, 18667, 29950, 2709, 34199

Offset: 1

Author

Torlach Rush, Dec 23 2020

Keywords

• nonn

Examples

			a(1) = 1 because there are 15 visible points from every point on the grid.
a(2) = 5 because 65 points are visible from every vertex of the grid, 73 points are visible from the midpoint of every edge of the grid, 77 points are visible from the midpoint of every face of the grid, 79 points are visible from the midpoint of every cell of the grid, and 80 points are visible from the middle of the grid.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Visible Point

Crossrefs

Cf. A339400, A339756.

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, 4)

Extensions

More terms from Bert Dobbelaere, Mar 20 2021