This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156816 #36 Dec 14 2024 09:18:01 %S A156816 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 A156816 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 A156816 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 A156816 Decimal expansion of the positive root of the equation 13x^4 - 7x^2 - 581 = 0. %C A156816 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 A156816 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.10, p. 331. %D A156816 N. Madras and G. Slade, The Self-Avoiding Walk (Boston, Birkhauser), 1993. %H A156816 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 A156816 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 A156816 Pierre-Louis Giscard, <a href="http://images-archive.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 A156816 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 A156816 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A156816 x = sqrt(7/26 + sqrt(30261)/26). %e A156816 x = 2.63815853034174086843... %t A156816 RealDigits[Sqrt[1/26*(7+Sqrt[30261])],10,120][[1]] (* _Harvey P. Dale_, Nov 22 2014 *) %o A156816 (PARI) polrootsreal(13*x^4-7*x^2-581)[2] \\ _Charles R Greathouse IV_, Apr 16 2014 %Y A156816 Cf. A001411, A002931, A179260, A249776. %K A156816 cons,nonn %O A156816 1,1 %A A156816 _Zak Seidov_, Feb 16 2009