OFFSET
2,1
COMMENTS
A concise description of the problem is given by Clive Tooth in the Seaman, Tooth link. Sequence terms up to n=10 were first given by Dave Seaman. Cubes having at least one vertex on the sphere and all other vertices either all inside or all outside the sphere are counted as 1/2. a(n) is asymptotic to (3/2)*Pi*n^2. (Clive Tooth) The terms a(2),...,a(6) are identical with A005897(n-1) (points on surface of cube with square grid on its faces).
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 2..1000
Hugo Pfoertner, FORTRAN program to count intersections.
Dave Seaman, Clive Tooth, Sphere/Cube Intersections. Discussion in Newsgroup sci.math.
EXAMPLE
a(2)=8 because all 8 cubes resulting from a 2*2*2 subdivision of a cube are intersected by a sphere inscribed in the large cube.
a(4)=56: 8 central cubes of 4*4*4=64 not intersected.
PROG
FORTRAN and C# programs are given at the links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jul 17 2003
EXTENSIONS
Corrected overflow in program and b-file by Hugo Pfoertner, Apr 09 2016
STATUS
approved