

A010575


Number of nstep selfavoiding walks on 4d cubic lattice.


13



1, 8, 56, 392, 2696, 18584, 127160, 871256, 5946200, 40613816, 276750536, 1886784200, 12843449288, 87456597656, 594876193016, 4047352264616, 27514497698984, 187083712725224, 1271271096363128, 8639846411760440, 58689235680164600, 398715967140863864
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



FORMULA



PROG

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


CROSSREFS



KEYWORD

nonn,walk,nice


AUTHOR



EXTENSIONS

a(18) onwards from R. J. Mathar using data from Clisby et al, Aug 31 2007


STATUS

approved



