A179261 Continued fraction expansion of the connective constant of the honeycomb lattice.

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

Offset

0,3

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

Paolo Xausa, Table of n, a(n) for n = 0..10000

Hugo Duminil-Copin and 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+.

Mathematica

ContinuedFraction[Sqrt[2 + Sqrt[2]], 100] (* Paolo Xausa, Aug 07 2024 *)

Prog

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

Crossrefs

Cf. A002193, A179260 (decimal expansion).

Sequence in context: A073050 A366426 A154740 * A154567 A260210 A139391

Adjacent sequences: A179258 A179259 A179260 * A179262 A179263 A179264

Keyword

cofr,nonn

Author

Jonathan Vos Post, Jul 06 2010

Extensions

Offset changed by Andrew Howroyd, Aug 07 2024

Status

approved