login
A210519
a(n) = floor(volume of 4-sphere of radius n).
1
0, 4, 78, 399, 1263, 3084, 6395, 11848, 20212, 32377, 49348, 72250, 102328, 140942, 189575, 249824, 323407, 412159, 518035, 643108, 789568, 959725, 1156007, 1380959, 1637248, 1927657, 2255086, 2622556, 3033205, 3490291
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.
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
Sequence in context: A273952 A370953 A201984 * A279437 A296997 A220240
KEYWORD
nonn
AUTHOR
Jon Perry, Jan 26 2013
STATUS
approved