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A164083 Ceiling of 2^(n-1) times the surface area of the unit sphere in 2n-dimensional space. 2
7, 40, 125, 260, 409, 513, 537, 482, 379, 265, 167, 95, 50, 25, 11, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The rounded values of this real sequence is A164082, the floor is A164081.

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

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..58.

Eric W. Weisstein, Hypersphere,

FORMULA

a(n) = ceiling(((2*pi)^n)/(n-1)!).

EXAMPLE

Table of approximate real values before rounding up.

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

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

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

MATHEMATICA

Table[Ceiling[(2Pi)^n/(n-1)!], {n, 60}] (* Harvey P. Dale, Jul 30 2020 *)

CROSSREFS

Cf. A072345, A072346, A072478, A072479, A074457, A122510, A154255, A164081, A164082.

Sequence in context: A249635 A164135 A119056 * A096200 A263473 A055282

Adjacent sequences:  A164080 A164081 A164082 * A164084 A164085 A164086

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Aug 09 2009

EXTENSIONS

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

STATUS

approved

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Last modified June 20 01:09 EDT 2021. Contains 345154 sequences. (Running on oeis4.)