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A164081 Floor of 2^(n-1) times the surface area of the unit sphere in 2n-dimensional space. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 09:51 EST 2023. Contains 359943 sequences. (Running on oeis4.)