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

Author

Hugo Pfoertner, Dec 14 2024

Keywords

• nonn
• cons
• hard
• more

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.

Examples

			3953.7...
		

Links

• 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).

Crossrefs

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