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A205326
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Decimal expansion of the sum of [0;n,n,n,...]^2 for n=1..infinity.
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1
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9, 1, 5, 5, 8, 7, 9, 1, 9, 9, 0, 1, 8, 1, 9, 7, 2, 5, 1, 9, 9, 8, 1, 6, 8, 5, 3, 8, 0, 3, 1, 9, 0, 0, 8, 9, 7, 3, 5, 3, 2, 0, 4, 6, 0, 1, 8, 9, 6, 6, 9, 0, 2, 4, 1, 2, 2, 7, 6, 9, 5, 1, 7, 0, 9, 6, 2, 1, 8, 2, 7, 0, 5, 5, 6, 4, 6, 5, 3, 3, 5, 9, 7, 5, 5, 3, 7
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OFFSET
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0,1
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COMMENTS
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This is the total area of all squares with sides parallel to the axes of the Cartesian coordinate system, the lower left vertex at (n,0) and the upper right vertex on f(x)=1/x for n=1..infinity.
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LINKS
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Table of n, a(n) for n=0..86.
Martin Janecke, Edle Reihe
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FORMULA
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Sum_{n>=1} 1/[n;n,n,...]^2.
Sum_{n>=1} 4/(n + sqrt(n^2 + 4))^2.
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EXAMPLE
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0.9155879199018197251998168538031900897353...
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PROG
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(PARI) zeta(2)+sumpos(n=1, 4/(n+sqrt(n^2+4))^2-1/n^2) \\ Charles R Greathouse IV, Jan 26 2012
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CROSSREFS
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Cf. A013661, A205325, continued fractions A001622, A014176, A098316, A098317, A098318.
Sequence in context: A258268 A143296 A198355 * A021526 A019791 A006752
Adjacent sequences: A205323 A205324 A205325 * A205327 A205328 A205329
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KEYWORD
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cons,nonn
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AUTHOR
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Martin Janecke, Jan 26 2012
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EXTENSIONS
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a(-5)-a(-86) from Charles R Greathouse IV, Jan 26 2012
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STATUS
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approved
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