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 A240946 #25 Sep 22 2023 11:59:28 %S A240946 1,5,7,4,5,9,7,2,3,7,5,5,1,8,9,3,6,5,7,4,9,4,6,9,2,1,8,3,0,7,6,5,1,9, %T A240946 6,9,0,2,2,1,6,6,6,1,8,0,7,5,8,5,1,9,1,7,0,1,9,3,6,9,3,0,9,8,3,0,1,8, %U A240946 3,1,1,8,0,5,9,4,4,5,4,3,8,2,1,3,1,0,8,5,3,1,3,3,6,2,2,4,1,9,5,3 %N A240946 Decimal expansion of the average distance traveled in three steps of length 1 for a random walk in the plane starting at the origin. %H A240946 J. M. Borwein, A. Straub, J. Wan, and W. Zudilin, <a href="http://arxiv.org/abs/1103.2995">Densities of short uniform random walks</a>, arXiv:1103.2995 [math.CA], (11-August-2011) %H A240946 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 464. %F A240946 Integral_(0..3) x*p(x) dx, where p(x) = 2*sqrt(3)/Pi*x/(3+x^2) * 2F1(1/3, 2/3; 1; x^2*(9-x^2)^2/(3+x^2)^3), 2F1 being the hypergeometric function. %F A240946 Re(3F2(-1/2, -1/2, 1/2; 1, 1; 4)). %F A240946 (3*2^(1/3))/(16*Pi^4)*Gamma(1/3)^6 + (27*2^(2/3))/(4*Pi^4)*Gamma(2/3)^6. %e A240946 1.5745972375518936574946921830765... %t A240946 (3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 + (27*2^(2/3))/(4*Pi^4)*Gamma[2/3]^6 // %t A240946 RealDigits[#, 10, 100]& // First (* updated May 20 2015 *) %Y A240946 Cf. A088538 (two steps). %K A240946 nonn,cons,walk %O A240946 1,2 %A A240946 _Jean-François Alcover_, Aug 04 2014 %E A240946 More digits from _Jean-François Alcover_, May 20 2015