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

1,2

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Visible Point

Example

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.

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, 4)

Crossrefs

Cf. A339400, A339756.

Sequence in context: A338085 A302676 A370297 * A206553 A122213 A224067

Adjacent sequences: A339944 A339945 A339946 * A339948 A339949 A339950

Keyword

nonn

Author

Torlach Rush, Dec 23 2020

Extensions

More terms from Bert Dobbelaere, Mar 20 2021

Status

approved