The number of regions into which space can be divided by 
mutually intersecting spheres is
 |
giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for 
,
2, ....
Space Division by Spheres
See also
Plane Division by Circles, Space Division by Planes, Sphere-Sphere IntersectionExplore with Wolfram|Alpha
References
Sloane, N. J. A. Sequence A046127 in "The On-Line Encyclopedia of Integer Sequences."Yaglom, A. M. and Yaglom, I. M. Challenging Mathematical Problems with Elementary Solutions, Vol. 1. New York: Dover, pp. 102-106, 1987.Referenced on Wolfram|Alpha
Space Division by SpheresCite this as:
Weisstein, Eric W. "Space Division by Spheres." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpaceDivisionbySpheres.html