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

Offset: 1

Author

Jean-François Alcover, Mar 10 2015

Keywords

• nonn
• cons
• easy

Examples

			4.4516506980892215382479987827401255099693875...
		

Links

• 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

Crossrefs

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

Programs

Mathematica

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

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.