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

Author

Eric W. Weisstein, Jul 12 2003

Keywords

• nonn
• cons

Examples

			0.19320167322498393734187097332936916057587338645...
		

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.

Crossrefs

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

Programs

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 *)

Formula

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

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