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A255902
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Decimal expansion of the limit as n tends to infinity of n*s_n, where the s_n are the hexagonal circle-packing rigidity constants.
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0
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4, 4, 5, 1, 6, 5, 0, 6, 9, 8, 0, 8, 9, 2, 2, 1, 5, 3, 8, 2, 4, 7, 9, 9, 8, 7, 8, 2, 7, 4, 0, 1, 2, 5, 5, 0, 9, 9, 6, 9, 3, 8, 7, 5, 0, 3, 9, 7, 4, 5, 7, 6, 8, 7, 3, 6, 3, 9, 6, 8, 6, 5, 2, 9, 9, 1, 9, 2, 4, 1, 3, 1, 8, 8, 3, 6, 0, 8, 6, 6, 4, 1, 2, 7, 5, 3, 0, 2, 3, 1, 7, 7, 8, 3, 7, 0, 0, 1, 3, 2, 9, 2
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..102.
P. Doyle, Zheng-Xu He, and B. Rodin, The asymptotic value of the circle-packing rigidity constants, Discrete Comput. Geom. 12 (1994).
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 68.
Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]
Eric Weisstein's MathWorld, Conformal Radius
Wikipedia, Circle packing theorem
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FORMULA
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(2^(4/3)/3)*gamma(1/3)^2/gamma(2/3).
Equals 4/R, where R = 2^(2/3)*gamma(2/3)/(gamma(1/3)*gamma(4/3)) is the conformal radius in a mapping from the unit disk to the unit side hexagon satisfying certain conditions.
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EXAMPLE
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4.4516506980892215382479987827401255099693875...
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MATHEMATICA
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RealDigits[(2^(4/3)/3)*Gamma[1/3]^2/Gamma[2/3], 10, 102] // First
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CROSSREFS
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Cf. A073005 (gamma(1/3)), A073006 (gamma(2/3)).
Sequence in context: A200694 A021696 A006581 * A019922 A092171 A179778
Adjacent sequences: A255899 A255900 A255901 * A255903 A255904 A255905
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Jean-François Alcover, Mar 10 2015
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STATUS
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approved
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