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Search: id:A114346
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| A114346 |
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The integer difference between n+1 dimensional surface area and n dimensional volume. |
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+0
1
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| 2, 1, 2, 7, 14, 21, 26, 29, 29, 27, 23, 19, 15, 11, 8, 5, 3, 2, 1, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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This sequence is important in the n dimensional ( topological dimension) theory of particles and has a maximum at n=8. I had noticed that at a given set of scale of radius there were near integer relationships between these two. q=(v[5]*e0)^(1/5) in esu ( electric charge) s[5]*q^4-v[4]*q^4 --> 3*G for G the gravitational constant.
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REFERENCES
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D.M.Y Sommerville, An Introduction to the Geometry of n dimensions,Dover Publications,1858, pages136-137
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FORMULA
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v[n_] = Pi^(n/2)/Gamma[n/2 + 1] s[n_] = 2*Pi^(n/2)/Gamma[n/2] a(n) = Floor[Abs[s[n] - v[n + 1]]]
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A056887 A144803 A095062 this_sequence A032068 A103410 A114303
Adjacent sequences: A114343 A114344 A114345 this_sequence A114347 A114348 A114349
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 08 2006
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