A255902 - OEIS

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.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

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: A021696 A006581 A370717 * A019922 A092171 A179778

Adjacent sequences: A255899 A255900 A255901 * A255903 A255904 A255905

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Mar 10 2015

STATUS

approved