A247447 Decimal expansion of r_(5,1), a constant which is the residue at -4 of the distribution function of the distance travelled in a 5-step uniform random walk.

0, 0, 6, 6, 1, 6, 7, 3, 0, 2, 5, 9, 4, 3, 0, 0, 8, 1, 7, 1, 4, 0, 5, 7, 7, 3, 8, 0, 0, 0, 7, 4, 9, 6, 5, 6, 2, 4, 9, 5, 5, 1, 0, 3, 2, 7, 5, 2, 4, 8, 3, 3, 0, 3, 9, 9, 7, 1, 5, 8, 3, 6, 3, 0, 8, 3, 2, 7, 5, 3, 4, 7, 2, 7, 1, 4, 0, 9, 2, 1, 2, 8, 0, 8, 2, 8, 0, 7, 7, 9, 0, 7, 6, 6, 9, 2, 9, 0, 4, 9, 1, 6, 4

Offset

0,3

Links

Table of n, a(n) for n=0..102.

Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 974, Canad. J. Math. 64(2012), 961-990.

Formula

r_(5,1) = 13/225*r_(5,0) - 2/(5*Pi^4*r_(5,0)), where r_(5,0) is A244995 (residue at -2).

r_(5,1) = 13/(1800*sqrt(5))*Gamma(1/15)*Gamma(2/15)*Gamma(4/15)*Gamma(8/15)/Pi^4 - 1/sqrt(5)*Gamma(7/15)*Gamma(11/15)*Gamma(13/15)*Gamma(14/15)/Pi^4.

Example

0.0066167302594300817140577380007496562495510327524833...

Mathematica

r[5, 0] = (2*Sqrt[15]*Re[HypergeometricPFQ[{1/2, 1/2, 1/2}, {5/6, 7/6}, 125/4]])/Pi^2; r[5, 1] = 13/225*r[5, 0] - 2/(5*Pi^4*r[5, 0]); Join[{0, 0}, RealDigits[r[5, 1], 10, 101] // First]

Crossrefs

Cf. A244993, A244994, A244995, A244996, A244997, A244999, A245025, A245026.

Sequence in context: A200281 A199864 A153605 * A112302 A073012 A102522

Adjacent sequences: A247444 A247445 A247446 * A247448 A247449 A247450

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Sep 17 2014

Status

approved