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A114348
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The integer difference between (the n-dimensional unit sphere surface area minus the (n+1)-dimensional unit sphere volume) and the (n+2)-dimensional unit sphere volume.
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1
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-6, -3, 2, 9, 16, 22, 25, 26, 25, 22, 18, 14, 10, 7, 5, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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D. M. Y Sommerville, An Introduction to the Geometry of n dimensions, Dover Publications (1958), pages 136-137.
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LINKS
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FORMULA
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Let v(n) = pi^(n/2)/Gamma(n/2+1) be the volume of the n-dimensional unit sphere and s(n) = 2*Pi^(n/2)/Gamma(n/2) be its surface content. Then a(n) = floor(s(n)-v(n+1)-v(n+2)).
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MATHEMATICA
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Table[Floor[ (Pi^(n/2)/2)*( (n*(n+2)-2*Pi)/Gamma[n/2 +2] - 2*Sqrt[Pi]/Gamma[(n+3)/2])], {n, 50}] (* G. C. Greubel, Feb 06 2021 *)
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CROSSREFS
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KEYWORD
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sign,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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