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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
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
Sequence in context: A351047 A289162 A164081 * A159571 A007793 A297579
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 24 06:47 EST 2024. Contains 370294 sequences. (Running on oeis4.)