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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.
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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