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A164082 Rounded value of 2^(n-1) times the surface area of the unit sphere in 2n-dimensional space. 3
6, 39, 124, 260, 408, 513, 537, 482, 379, 264, 166, 95, 50, 24, 11, 5, 2, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The floor of this real sequence is A164081, the ceiling is A164083.

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

There are 18 nonzero terms in this sequence. - G. C. Greubel, Sep 11 2017

REFERENCES

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

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

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

LINKS

Table of n, a(n) for n=1..50.

Eric W. Weisstein, Hypersphere,

FORMULA

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

EXAMPLE

Table of approximate real values before rounding up or down:

========================

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

A164082 := proc(n) (2*Pi)^n/(n-1)! ; round(%) ; end: seq(A164082(n), n=1..80) ; # R. J. Mathar, Sep 09 2009

MATHEMATICA

Table[Round[(2*Pi)^n/(n - 1)!], {n, 1, 20}] (* G. C. Greubel, Sep 11 2017 *)

PROG

(PARI) for(n=1, 20, print1(round((2*Pi)^n/(n-1)!), ", ")) \\ G. C. Greubel, Sep 11 2017

CROSSREFS

Cf. A072345, A072346, A072478, A072479, A074457, A122510, A154255, A164081, A164083.

Sequence in context: A351047 A289162 A164081 * A159571 A007793 A297579

Adjacent sequences: A164079 A164080 A164081 * A164083 A164084 A164085

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 February 8 16:04 EST 2023. Contains 360149 sequences. (Running on oeis4.)