Space Division

The number of regions into which space can be divided by $n$ Spheres is

$$N={\textstyle{1\over 3}} n(n^2-3n+8),$$

giving 2, 4, 8, 16, 30, 52, 84, ... (Sloane's A046127).

See also Plane Division

References

Sloane, N. J. A. Sequence A046127 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.