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A244847 Decimal expansion of rho_c = (5-sqrt(5))/10, the asymptotic critical density for the hard hexagon model. 0
2, 7, 6, 3, 9, 3, 2, 0, 2, 2, 5, 0, 0, 2, 1, 0, 3, 0, 3, 5, 9, 0, 8, 2, 6, 3, 3, 1, 2, 6, 8, 7, 2, 3, 7, 6, 4, 5, 5, 9, 3, 8, 1, 6, 4, 0, 3, 8, 8, 4, 7, 4, 2, 7, 5, 7, 2, 9, 1, 0, 2, 7, 5, 4, 5, 8, 9, 4, 7, 9, 0, 7, 4, 3, 6, 2, 1, 9, 5, 1, 0, 0, 5, 8, 5, 5, 8, 5, 5, 9, 1, 6, 2, 1, 2, 1, 7, 7, 2, 5, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.12.1 Phase transitions in Lattice Gas Models, p. 347.

LINKS

Table of n, a(n) for n=0..101.

Rodney J. Baxter Hard hexagons: exact solution, Journal of Physics A: Mathematical and General, Vol. 13, No. 3 (1980), pp. L61-L70, alternative link.

P. S. Bruckman and I. J. Good, A Generalization of a Series of De Morgan with Applications of Fibonacci Type, The Fibonacci Quarterly, Vol. 14, No. 3 (1976), pp. 193-196.

Eric Weisstein's MathWorld, Hard Hexagon Entropy Constant

Wikipedia, Hard Hexagon Model

FORMULA

Equals 1/(sqrt(5)*phi), where phi = (1+sqrt(5))/2 = A001622. - Vaclav Kotesovec, Nov 13 2014

Equals lim_{n -> infinity} A000045(n)/A000032(n+1). - Bruno Berselli, Jan 22 2018

Equals Sum_{n>=1} A000045(3^(n-1))/A000032(3^n) = Sum_{n>=1} A045529(n-1)/A006267(n). - Amiram Eldar, Dec 20 2018

EXAMPLE

0.2763932022500210303590826331268723764559381640388474275729102754589479...

MATHEMATICA

RealDigits[(5 - Sqrt[5])/10, 10, 102] // First

CROSSREFS

Cf. A244593.

Cf. A000032, A000045.

Sequence in context: A021366 A135155 A308705 * A175477 A011263 A074067

Adjacent sequences:  A244844 A244845 A244846 * A244848 A244849 A244850

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Nov 12 2014

STATUS

approved

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Last modified October 18 13:31 EDT 2019. Contains 328161 sequences. (Running on oeis4.)