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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..29.

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

Cf. A066643, A066645.

Sequence in context: A006267 A273952 A201984 * A279437 A296997 A220240

Adjacent sequences:  A210516 A210517 A210518 * A210520 A210521 A210522

KEYWORD

nonn

AUTHOR

Jon Perry, Jan 26 2013

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)