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Search: id:A072478
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| A072478 |
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Surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1) = n*Pi^(n/2)*r^(n-1)/(n/2)! = S_n*Pi^floor(n/2)*r^(n-1); sequence gives numerator of S_n. |
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5
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| 0, 2, 2, 4, 2, 8, 1, 16, 1, 32, 1, 64, 1, 128, 1, 256, 1, 512, 1, 1024, 1, 2048, 1, 4096, 1, 8192, 1, 16384, 1, 32768, 1, 65536, 1, 131072, 1, 262144, 1, 524288, 1, 1048576, 1, 2097152, 1, 4194304, 1, 8388608, 1, 16777216, 1, 33554432, 1, 67108864, 1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Answer to question of how to extend the sequence 0, 2, 2 Pi r, 4 Pi r^2, 2 Pi^2 r^3, ...
Volume of n-dimensional sphere of radius r is V_n*r^n - see A072345/A072346.
a(2n-1) = 2^n and for n>2 a(2n)=1.
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 10, Eq. 19.
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LINKS
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Eric Weisstein's World of Mathematics, Ball
Eric Weisstein's World of Mathematics, Hypersphere
Eric Weisstein's World of Mathematics, Four-Dimensional Geometry
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EXAMPLE
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Sequence of S_n's begins 0, 2, 2, 4, 2, 8/3, 1, 16/15, 1/3, 32/105, 1/12, 64/945, ...
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MATHEMATICA
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f[n_] := Pi^(n/2 - Floor[n/2])*n/(n/2)!; Table[ Numerator[ f[n]], {n, 0, 52}]
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CROSSREFS
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Cf. A072479. A072478(n)/A072479(n) = n*A072345(n)/A072346(n).
Sequence in context: A122977 A003980 A132801 this_sequence A100577 A018818 A067538
Adjacent sequences: A072475 A072476 A072477 this_sequence A072479 A072480 A072481
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KEYWORD
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nonn,frac,easy
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AUTHOR
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njas, Aug 02 2002
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 18 2002
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