

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.


1



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, 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, 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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..100.
J. M. Borwein, A. Straub, J. Wan, and W. Zudilin, Densities of short uniform random walks, arXiv:1103.2995 [math.CA], (11August2011)


FORMULA

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*(9x^2)^2/(3+x^2)^3), 2F1 being the hypergeometric function.
Re(3F2(1/2, 1/2, 1/2; 1, 1; 4)).
(3*2^(1/3))/(16*Pi^4)*Gamma(1/3)^6 + (27*2^(2/3))/(4*Pi^4)*Gamma(2/3)^6.


EXAMPLE

1.5745972375518936574946921830765...


MATHEMATICA

(3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 + (27*2^(2/3))/(4*Pi^4)*Gamma[2/3]^6 //
RealDigits[#, 10, 100]& // First (* updated May 20 2015 *)


CROSSREFS

Cf. A088538 (two steps).
Sequence in context: A010488 A300081 A293843 * A343039 A021178 A201506
Adjacent sequences: A240943 A240944 A240945 * A240947 A240948 A240949


KEYWORD

nonn,cons,walk


AUTHOR

JeanFrançois Alcover, Aug 04 2014


EXTENSIONS

More digits from JeanFrançois Alcover, May 20 2015


STATUS

approved



