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%I #31 Nov 06 2023 03:41:50
%S 2,6,3,8,1,5,8,5,3,0,3,4,1,7,4,0,8,6,8,4,3,0,3,0,7,5,6,6,7,4,4,4,1,3,
%T 0,4,8,8,8,0,5,0,2,2,0,1,0,3,1,8,3,5,9,7,3,7,0,7,8,7,0,6,0,7,7,6,9,6,
%U 3,2,1,9,7,0,7,3,5,5,9,5,9,8,8,9,3,2,0,0,5,1,8,9,0,0,0,9,8,3,3,5,2,4,2,1,2
%N Decimal expansion of the positive root of the equation 13x^4 - 7x^2 - 581 = 0.
%C This constant approximates the connective constant of the square lattice, which is known only numerically, but "no derivation or explanation of this quartic polynomial is known, and later evidence has raised doubts about its validity" [Bauerschmidt et al, 2012, p. 4]. - _Andrey Zabolotskiy_, Dec 26 2018
%D N. Madras and G. Slade, The Self-Avoiding Walk (Boston, Birkhauser), 1993.
%H Roland Bauerschmidt, Hugo Duminil-Copin, Jesse Goodman, and Gordon Slade, <a href="https://arxiv.org/abs/1206.2092">Lectures on Self-Avoiding Walks</a>, arXiv:1206.2092 [math.PR], 2012.
%H M. Bousquet-Mélou, A. J. Guttmann and I. Jensen, <a href="http://arxiv.org/abs/cond-mat/0506341">Self-avoiding walks crossing a square</a>, arXiv:cond-mat/0506341, 2005.
%H Pierre-Louis Giscard, <a href="http://images.math.cnrs.fr/Que-sait-on-compter-sur-un-graphe-Partie-3.html">Que sait-on compter sur un graphe. Partie 3</a> (in French), Images des Mathématiques, CNRS, 2020.
%H Jesper Lykke Jacobsen, Christian R. Scullard, and Anthony J. Guttmann, <a href="https://doi.org/10.1088/1751-8113/49/49/494004">On the growth constant for square-lattice self-avoiding walks</a>, J. Phys. A: Math. Theor., 49 (2016), 494004; arXiv:<a href="https://arxiv.org/abs/1607.02984">1607.02984</a> [cond-mat.stat-mech], 2016.
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F x = sqrt(7/26 + sqrt(30261)/26).
%e x = 2.63815853034174086843...
%t RealDigits[Sqrt[1/26*(7+Sqrt[30261])],10,120][[1]] (* _Harvey P. Dale_, Nov 22 2014 *)
%o (PARI) polrootsreal(13*x^4-7*x^2-581)[2] \\ _Charles R Greathouse IV_, Apr 16 2014
%Y Cf. A001411, A002931, A179260, A249776.
%K cons,nonn
%O 1,1
%A _Zak Seidov_, Feb 16 2009
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