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Search: id:A114348
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| A114348 |
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The integer difference between n+1 dimensional volume and the n+1 dimensional surface area and the n dimensional volume. |
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+0
2
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| 5, 5, 2, 2, 9, 16, 22, 25, 26, 25, 22, 18, 14, 10, 7, 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 near 8*Pi.
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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[v[n + 1] - (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[v[n + 2] - (s[n] - v[n + 1])]], {n, 0, 20}]
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CROSSREFS
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Sequence in context: A092766 A060074 A011501 this_sequence A125642 A011335 A021185
Adjacent sequences: A114345 A114346 A114347 this_sequence A114349 A114350 A114351
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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; corrected Feb 08 2006
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