A378903 Decimal expansion of the expected number of steps to termination by self-trapping of a self-avoiding random walk on the cubic lattice.

3, 9, 5, 3, 7

Offset

4,1

Comments

See A077818 for more information and links. Since a more accurate value is probably 3953.78..., one should currently use 3953.8 +- 0.1 as a safe estimate.

Links

Table of n, a(n) for n=4..8.

Martin Z. Bazant, Topics in Random Walks and Diffusion, Graduate course 18.325, Spring 2001 at the Massachusetts Institute for Technology.

Martin Z. Bazant, Topics in Random Walks and Diffusion, Problem Sets for Spring 2001. In the no longer available solutions to Problem Set 2b, Dion Harmon gave 3960 using 10^5 walks, and E.C.Silva gave 3676 using 1.5*10^4 walks.

Martin Z. Bazant, Problem Set 2 for Graduate course 18.325, local pdf version of postscript file. Problem 5. Self-Trapping Walk.

Hugo Pfoertner, Probability density for the number of steps before trapping occurs, based on 27*10^9 simulated walks (2024).

Example

3953.7...

Crossrefs

Cf. A001412, A077817, A077818, A077819, A077820, A377161, A377162.

Sequence in context: A021257 A358190 A282529 * A070341 A245719 A085851

Adjacent sequences: A378900 A378901 A378902 * A378909 A378910 A378911

Keyword

nonn,cons,hard,more,new

Author

Hugo Pfoertner, Dec 14 2024

Status

approved