A164081 Floor of 2^(n-1) times the surface area of the unit sphere in 2n-dimensional space.

6, 39, 124, 259, 408, 512, 536, 481, 378, 264, 166, 94, 49, 24, 10, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

The rounded values of this real sequence is A164082, the ceiling is A164083.

The surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1); see A072478/A072479.

There are only 17 nonzero terms. - G. C. Greubel, Sep 10 2017

References

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices, and Groups, 2nd ed., New York: Springer-Verlag, p. 9, 1993.

H. S. M. Coxeter, Regular Polytopes, 3rd ed., New York: Dover, 1973.

D. M. Y. Sommerville, An Introduction to the Geometry of n Dimensions, New York: Dover, p. 136, 1958.

Links

Table of n, a(n) for n=1..59.

Eric W. Weisstein, Hypersphere.

Formula

a(n) = floor( (2*Pi)^n/(n-1)! ).

Example

Table of approximate real values before taking integer part.
========================
n (2*Pi)^n / (n-1)!
1 6.28318531 = A019692
2 39.4784176 = 2*A164102
3 124.025107 = 4*A091925
4 259.757576 = 8*A164109
5 408.026246
6 512.740903
7 536.941018
8 481.957131
9 378.528246
10 264.262568
11 166.041068
12 94.8424365
13 49.6593836
14 24.00147
15 10.7718345
16 4.5120955
17 1.77189576
18 0.654891141
19 0.228600133
20 0.075596684
========================

Maple

A164081 := proc(n) (2*Pi)^n/(n-1)! ; floor(%) ; end: seq(A164081(n), n=1..80) ; # R. J. Mathar, Sep 09 2009

Mathematica

Table[Floor[(2*Pi)^n/(n - 1)!], {n, 1, 100}] (* G. C. Greubel, Sep 10 2017 *)

Prog

(PARI) for(n=1, 100, print1(floor((2*Pi)^n/(n-1)!), ", ")) \\ G. C. Greubel, Sep 10 2017

Crossrefs

Cf. A072345, A072346, A072478, A072479, A074457, A122510, A154255.

Sequence in context: A220855 A351047 A289162 * A164082 A159571 A007793

Adjacent sequences: A164078 A164079 A164080 * A164082 A164083 A164084

Keyword

nonn

Author

Jonathan Vos Post, Aug 09 2009

Extensions

Definition corrected by R. J. Mathar, Sep 09 2009

Status

approved