The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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