OFFSET
0,2
COMMENTS
The 4-sphere here refers to the geometric sphere, that is, 4 refers to the number of dimensions of the sphere.
The general formula for the volume of an n-sphere can be derived using (4)-(10) at the Mathworld link, and some explicit values for higher dimensional spheres are given at the Wikipedia link, section 2.4. Note that Wikipedia uses the topologic definition and calls this 4-sphere a 3-sphere.
LINKS
Clay Math Institute, Poincaré Conjecture Press Release
Mathworld, Hypersphere
Mathworld, Poincaré's Conjecture
Wikipedia, N-sphere
FORMULA
a(n) = floor(1/2*Pi^2*n^4).
MATHEMATICA
Table[Floor[(Pi^2 n^4)/2], {n, 0, 29}]
PROG
(JavaScript)
pi = Math.PI;
for (i = 0; i < 60; i++) document.write(Math.floor(pi*pi*i*i*i*i/2) + ", ");
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Jan 26 2013
STATUS
approved