A239318 Number of visible unit cubes, aligned with a three-dimensional Cartesian mesh, completely within the first octant of a sphere centered at the origin, ordered by increasing radius.

1, 3, 6, 6, 7, 10, 12, 12, 15, 15, 18, 18, 21, 22, 25, 25, 28, 30, 30, 33, 33, 36, 39, 39, 39, 42, 42, 43, 43, 46, 49, 49, 52, 52, 54, 57, 57, 60, 63, 66, 66, 66, 66, 69, 69, 72, 72, 73, 76, 79, 79, 82, 82, 82, 82, 87, 90, 93, 93, 93, 93, 96, 96, 99, 99, 102

Offset: 1

Author

Frans Faase, Mar 15 2014

Keywords

• nonn

Comments

This sequence is related to A237707, which gives all unit cubes. For each element in that sequence, this sequence gives the number of cubes that have at least one side that is visible from the sphere.

Crossrefs

Cf. A237707.

Programs

C

void printVisibleCubes(int nr)
{
    int prev_c = 0;
    for (int r = 3; nr > 0; r++)
    {
        int c = 0;
        int c2 = 0;
        for (int i = 1; i*i + 2 <= r; i++)
            for (int j = 1; i*i + j*j + 1 <= r; j++)
                for (int k = 1; i*i + j*j + k*k <= r; k++)
                {
                    c++;
                    if (   (i+1)*(i+1) + j*j + k*k > r
                        || i*i + (j+1)*(j+1) + k*k > r
                        || i*i + j*j + (k+1)*(k+1) > r)
                        c2++;
                }
        if (c > prev_c)
        {
            // c contains next element of A237707
            printf("%d, ", c2);
            prev_c = c;
            nr--;
        }
    }
}