

A255902


Decimal expansion of the limit as n tends to infinity of n*s_n, where the s_n are the hexagonal circlepacking rigidity constants.


0



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

1,1


LINKS

Table of n, a(n) for n=1..102.
P. Doyle, ZhengXu He, and B. Rodin, The asymptotic value of the circlepacking 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


FORMULA

(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.


EXAMPLE

4.4516506980892215382479987827401255099693875...


MATHEMATICA

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


CROSSREFS

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


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Mar 10 2015


STATUS

approved



