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Search: id:A072345
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| A072345 |
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Volume of n-dimensional sphere of radius r is V_n*r^n = Pi^(n/2)*r^n/(n/2)! = C_n*Pi^floor(n/2)*r^n; sequence gives numerator of C_n. |
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12
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| 1, 2, 1, 4, 1, 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, 134217728, 1, 268435456
(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 1, 2 r, Pi r^2, 4 Pi r^3 / 3, Pi^2 r^4 / 2, ...
Surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1). - see A072478/A072479.
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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. 9, Eq. 17.
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LINKS
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Eric Weisstein's World of Mathematics, Hypersphere
Eric Weisstein's World of Mathematics, Ball
Eric Weisstein's World of Mathematics, Four-Dimensional Geometry
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FORMULA
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1 if n even, 2^((n+1)/2) if n odd.
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EXAMPLE
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Sequence of C_n's begins 1, 2, 1, 4/3, 1/2, 8/15, 1/6, 16/105, 1/24, 32/945, 1/120, 64/10395, ...
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MAPLE
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seq(seq(k^n, k=1..2), n=1..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 29 2007
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MATHEMATICA
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f[n_] := Pi^(n/2 - Floor[n/2])/(n/2)!; Table[ Numerator[ f[n]], {n, 0, 55} ]
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CROSSREFS
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Cf. A072346.
Sequence in context: A115124 A115122 A097360 this_sequence A115120 A147373 A147441
Adjacent sequences: A072342 A072343 A072344 this_sequence A072346 A072347 A072348
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jul 31 2002
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