

A010575


Number of nstep selfavoiding walks on 4d cubic lattice.


12



1, 8, 56, 392, 2696, 18584, 127160, 871256, 5946200, 40613816, 276750536, 1886784200, 12843449288, 87456597656, 594876193016, 4047352264616, 27514497698984, 187083712725224, 1271271096363128, 8639846411760440, 58689235680164600, 398715967140863864
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OFFSET

0,2


COMMENTS

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 link below]
N. Clisby, R. Liang and G. Slade Selfavoiding walk enumeration via the lace expansion J. Phys. A: Math. Theor. vol. 40 (2007) p 1097311017, Table A6 for n<=24.
M. E. Fisher and D. S. Gaunt, Ising model and selfavoiding walks on hypercubical lattices and high density expansions, Phys. Rev. 133 (1964) A224A239.
D. MacDonald, D. L. Hunter, K. Kelly and N. Jan, Selfavoiding walks in two to five dimensions: exact enumerations and series study, J Phys A: Math Gen 25 (1992) Vol. 6, 14291440 [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), 10831108.
Hugo Pfoertner, Results for the 4D SelfTrapping Random Walk
Eric Weisstein's World of Mathematics, SelfAvoiding Walk Connective Constant


PROG

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


CROSSREFS

Cf. A001411, A001412, A242355, A323856, A323857.
Sequence in context: A001666 A214942 A010556 * A162949 A063812 A234274
Adjacent sequences: A010572 A010573 A010574 * A010576 A010577 A010578


KEYWORD

nonn,walk,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

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, Dec 14 2002
More terms from Hugo Pfoertner, Dec 14 2002; Oct 19 2004
Further terms from R. J. Mathar, Aug 31 2007


STATUS

approved



