A242761 Decimal expansion of the escape probability for a random walk on the 3-D cubic lattice (a Polya random walk constant).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9, p. 322.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's MathWorld, Polya's Random Walk Constants

Formula

Equals (16*sqrt(2/3)*Pi^3)/(Gamma(1/24)*Gamma(5/24)*Gamma(7/24)*Gamma(11/24)), where Gamma is the Euler Gamma function.

Example

0.6594626704490008571737268155670971...

Mathematica

p = (16*Sqrt[2/3]*Pi^3)/(Gamma[1/24]*Gamma[5/24]*Gamma[7/24]*Gamma[11/24]); RealDigits[p, 10, 100] // First

Prog

(PARI) default(realprecision, 100); (16*sqrt(2/3)*Pi^3)/(gamma(1/24)* gamma(5/24)*gamma(7/24)*gamma(11/24)) \\ G. C. Greubel, Oct 26 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (16*Sqrt(2/3)*Pi(R)^3)/(Gamma(1/24)*Gamma(5/24)*Gamma(7/24)*Gamma(11/24)); // G. C. Greubel, Oct 26 2018

Crossrefs

Cf. A086230, A086231, A086232-A086236, A043546, A293237, A293238, A242812-A242816.

Sequence in context: A196760 A199949 A165227 * A200477 A269768 A073230

Adjacent sequences: A242758 A242759 A242760 * A242762 A242763 A242764

Keyword

nonn,cons

Author

Jean-François Alcover, May 22 2014

Status

approved