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A179261 Continued fraction expansion of the connective constant of the honeycomb lattice. 0
1, 1, 5, 1, 1, 3, 6, 1, 3, 3, 10, 10, 1, 1, 1, 5, 2, 3, 1, 1, 3, 6, 1, 8, 74, 2, 1, 2, 4, 2, 4, 3, 5, 9, 4, 3, 1, 1, 1, 2, 1, 17, 6, 1, 2, 12, 1, 1, 1, 2, 1, 24, 1, 2, 1, 2, 9, 989, 2, 13, 1, 5, 1, 1, 1, 64, 2, 2, 1, 1, 9, 1, 3, 1, 1, 1, 2, 3, 11, 2, 3, 1, 10, 16, 2, 1, 2, 6, 4, 2, 3, 3, 3, 4, 1, 151, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Essentially the same as A154740 because the associated constants obey 1/A154739 = A179260. - R. J. Mathar, Jul 11 2010

REFERENCES

N. Madras and G. Slade, Self-avoiding walks, Probability and its Applications. Birkhäuser Boston, Inc. Boston, MA (1993).

LINKS

Table of n, a(n) for n=1..99.

Hugo Duminil-Copin, Stanislav Smirnov, The connective constant of the honeycomb lattice equals sqrt(2+sqrt2), arXiv:1007.0575 [math-ph], 2010-2011.

G. Lawler, O. Schramm and W. Werner, On the scaling limit of planar self-avoiding walk, arXiv:math/0204277 [math.PR], 2002.

B. Nienhuis, Exact critical point and critical exponents of O(n) models in two dimensions, Phys. Rev. Lett. 49 (1982), 1062-1065.

EXAMPLE

1.8477590650225735... = 1 + 1/1+ 1/5+ 1/1+ 1/1+ 1/3+ 1/6+ 1/1+ 1/3+ 1/3+ 1/10+ 1/10+.

PROG

(PARI) contfrac(sqrt(2+sqrt(2))) \\ Michel Marcus, Mar 17 2018

CROSSREFS

Cf. A002193, A179260 (decimal expansion).

Sequence in context: A010129 A073050 A154740 * A154567 A260210 A139391

Adjacent sequences:  A179258 A179259 A179260 * A179262 A179263 A179264

KEYWORD

cofr,nonn

AUTHOR

Jonathan Vos Post, Jul 06 2010

STATUS

approved

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Last modified October 19 04:11 EDT 2019. Contains 328211 sequences. (Running on oeis4.)