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Search: id:A164081
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| A164081 |
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Floor of 2^(n-1) times the surface area of the unit sphere in 2n-dimensional space. |
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+0
3
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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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.
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LINKS
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Eric W. Weisstein, Hypersphere,
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FORMULA
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a(n) = floor( (2*pi)^n/(n-1)! ).
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EXAMPLE
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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
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MAPLE
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A164081 := proc(n) (2*Pi)^n/(n-1)! ; floor(%) ; end: seq(A164081(n), n=1..80) ; # R. J. Mathar, Sep 09 2009
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CROSSREFS
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Cf. A072345, A072346, A072478, A072479, A074457, A122510, A154255.
Sequence in context: A058985 A116951 A163737 this_sequence A164082 A159571 A007793
Adjacent sequences: A164078 A164079 A164080 this_sequence A164082 A164083 A164084
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 09 2009
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EXTENSIONS
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Definition corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2009
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