OFFSET
1,2
COMMENTS
This sequence is important in the n dimensional (topological dimension) theory of particles and has a maximum at n=8.
REFERENCES
D. M. Y Sommerville, An Introduction to the Geometry of n dimensions, Dover Publications, 1958, pages 136-137.
LINKS
Zhuorui He, Table of n, a(n) for n = 1..1000
Wikipedia, N-sphere
FORMULA
Let S(n) = 2*Pi^((n+1)/2)/Gamma((n+1)/2) and V(n) = Pi^(n/2)/Gamma(n/2+1). Then a(n) = floor|S(n-1)-V(n+1)|.
MAPLE
sar := proc(n)
2*Pi^((n+1)/2)/GAMMA((n+1)/2) ;
end proc:
vol := proc(n)
Pi^(n/2)/GAMMA(n/2+1) ;
end proc:
A114346 := proc(n)
floor(abs(sar(n-1)-vol(n+1))) ;
end proc: # R. J. Mathar, Mar 05 2016
MATHEMATICA
v[n_]=Pi^(n/2)/Gamma[n/2+1] s[n_]=2*Pi^(n/2)/Gamma[n/2] a=Table[Floor[Abs[s[n]-v[n+1]]], {n, 0, 20}]
PROG
(PARI) A114346(n)=floor(abs(2*Pi^(n/2)/gamma(n/2)-Pi^((n+1)/2)/gamma((n+1)/2+1))) \\ Zhuorui He, Oct 31 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Feb 08 2006
EXTENSIONS
More terms from Zhuorui He, Oct 31 2025
STATUS
approved
