OFFSET
1,1
COMMENTS
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) = 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
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Aug 09 2009
EXTENSIONS
Definition corrected - R. J. Mathar, Sep 09 2009
STATUS
approved