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A255902 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. 0

%I

%S 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,

%T 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,

%U 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

%N 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.

%H P. Doyle, Zheng-Xu He, and B. Rodin, <a href="http://dx.doi.org/10.1007/BF02574369">The asymptotic value of the circle-packing rigidity constants</a>, Discrete Comput. Geom. 12 (1994).

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 68.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ConformalRadius.html">Conformal Radius</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Circle_packing_theorem">Circle packing theorem</a>

%F (2^(4/3)/3)*gamma(1/3)^2/gamma(2/3).

%F 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.

%e 4.4516506980892215382479987827401255099693875...

%t RealDigits[(2^(4/3)/3)*Gamma[1/3]^2/Gamma[2/3], 10, 102] // First

%Y Cf. A073005 (gamma(1/3)), A073006 (gamma(2/3)).

%K nonn,cons,easy,changed

%O 1,1

%A _Jean-Fran├žois Alcover_, Mar 10 2015

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Last modified January 28 07:07 EST 2020. Contains 331317 sequences. (Running on oeis4.)