|
| |
|
|
A114348
|
|
The integer difference between (the n-dimensional unit sphere surface area minus the (n+1)-dimensional unit sphere volume) and the (n+2)-dimensional unit sphere volume.
|
|
1
|
|
|
|
-6, -3, 2, 9, 16, 22, 25, 26, 25, 22, 18, 14, 10, 7, 5, 3, 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, 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
|
|
|
|
REFERENCES
|
D. M. Y Sommerville, An Introduction to the Geometry of n dimensions, Dover Publications (1958), pages 136-137.
|
|
|
LINKS
|
|
|
|
FORMULA
|
Let v(n) = pi^(n/2)/Gamma(n/2+1) be the volume of the n-dimensional unit sphere and s(n) = 2*Pi^(n/2)/Gamma(n/2) be its surface content. Then a(n) = floor(s(n)-v(n+1)-v(n+2)).
|
|
|
MATHEMATICA
|
Table[Floor[ (Pi^(n/2)/2)*( (n*(n+2)-2*Pi)/Gamma[n/2 +2] - 2*Sqrt[Pi]/Gamma[(n+3)/2])], {n, 50}] (* G. C. Greubel, Feb 06 2021 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign,less
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
