OFFSET
0,2
COMMENTS
The computation for n=16 took 11.5 days CPU time on a 500MHz Digital Alphastation. The asymptotic behavior lim n->infinity a(n)/mu^n=const is discussed in the MathWorld link. The Pfoertner link provides an illustration of the asymptotic behavior indicating that the connective constant mu is in the range [6.79,6.80]. - Hugo Pfoertner, Dec 14 2002
Computation of the new term a(17) took 16.5 days CPU time on a 1.5GHz Intel Itanium 2 processor. - Hugo Pfoertner, Oct 19 2004
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 0..24 [from the Clisby et al. link below]
N. Clisby, R. Liang, and G. Slade, Self-avoiding walk enumeration via the lace expansion, J. Phys. A: Math. Theor., vol. 40 (2007), p. 10973-11017, Table A6 for n <= 24.
Nathan Clisby, Monte Carlo study of four-dimensional self-avoiding walks of up to one billion steps, arXiv:1703.10557 [cond-mat.stat-mech], 30 Mar 2017.
M. E. Fisher and D. S. Gaunt, Ising model and self-avoiding walks on hypercubical lattices and high density expansions, Phys. Rev. 133 (1964) A224-A239.
D. MacDonald, D. L. Hunter, K. Kelly, and N. Jan, Self-avoiding walks in two to five dimensions: exact enumerations and series study, J Phys A: Math Gen 25 (1992) Vol. 6, 1429-1440 [Gives 18 terms]
A. M. Nemirovsky et al., Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108.
Hugo Pfoertner, Results for the 4D Self-Trapping Random Walk
Eric Weisstein's World of Mathematics, Self-Avoiding Walk Connective Constant
FORMULA
a(n) = 8*A366925(n) for n >= 1. - Hugo Pfoertner, Nov 03 2023
PROG
(Fortran) c A "brute force" Fortran program to count the 4D walks is available at the Pfoertner link.
CROSSREFS
KEYWORD
nonn,walk,nice
AUTHOR
EXTENSIONS
a(12)-a(16) from Hugo Pfoertner, Dec 14 2002
a(17) from Hugo Pfoertner, Oct 19 2004
a(18) onwards from R. J. Mathar using data from Clisby et al, Aug 31 2007
STATUS
approved