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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
| D.M.Y Sommerville, An Introduction to the Geometry of n dimensions,Dover Publications,1858, pages136-137
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FORMULA
| 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
| 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
| Sequence in context: A060074 A011501 A196614 * A172125 A125642 A011335
Adjacent sequences: A114345 A114346 A114347 * A114349 A114350 A114351
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 08 2006; corrected Feb 08 2006
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