A086232 Decimal expansion of probability that a random walk on a 4-d lattice returns to the origin.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.9, p. 323.

Links

Marc Mezzarobba, Table of n, a(n) for n = 0..9999

Eric Weisstein's World of Mathematics, Pólya's Random Walk Constants.

Formula

Equals 1 - 1/A242812. - Amiram Eldar, Aug 28 2020

Example

0.19320167322498393734187097332936916057587338645...

Mathematica

First[RealDigits[1 - 1/NIntegrate[BesselI[0, t/4]^4 * Exp[ -t], {t, 0, Infinity}, PrecisionGoal->50, WorkingPrecision->350]]] (* Ryan Propper, Jul 12 2005 *)

Crossrefs

Cf. A086230, A086233, A086234, A086235, A086236, A242812.

Sequence in context: A250091 A199152 A306808 * A133867 A210113 A195704

Adjacent sequences: A086229 A086230 A086231 * A086233 A086234 A086235

Keyword

nonn,cons,changed

Author

Eric W. Weisstein, Jul 12 2003

Extensions

More terms from Ryan Propper, Jul 12 2005

a(51) corrected and more terms using the data at A242812 added by Amiram Eldar, Aug 28 2020

Status

approved