0,2

Extended to n=16. 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 (hugo(AT)pfoertner.org), Dec 14 2002

Computation of the new term a(17) took 16.5 days CPU time on an 1.5GHz Intel Itanium 2 processor. - Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 19 2004

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.

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, Section from World of Mathematics

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]

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.

A "brute force" FORTRAN program to count the 4D walks is available at the Pfoertner link.

Sequence in context: A002914 A001666 A010556 this_sequence A063812 A003950 A033134

Adjacent sequences: A010572 A010573 A010574 this_sequence A010576 A010577 A010578

nonn,walk,nice

njas

More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 14 2002; Oct 19 2004

Further terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 31 2007