%I
%S 1,8,56,392,2696,18584,127160,871256,5946200,40613816,276750536,
%T 1886784200,12843449288,87456597656,594876193016,4047352264616,
%U 27514497698984,187083712725224,1271271096363128,8639846411760440,58689235680164600,398715967140863864
%N Number of nstep selfavoiding walks on 4d cubic lattice.
%C 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
%H Hugo Pfoertner, <a href="/A010575/b010575.txt">Table of n, a(n) for n = 0..24</a> [from the Clisby link below]
%H N. Clisby, R. Liang and G. Slade <a href="http://dx.doi.org/10.1088/17518113/40/36/003">Selfavoiding walk enumeration via the lace expansion</a> J. Phys. A: Math. Theor. vol. 40 (2007) p 1097311017, Table A6 for n<=24.
%H M. E. Fisher and D. S. Gaunt, <a href="http://dx.doi.org/10.1103/PhysRev.133.A224">Ising model and selfavoiding walks on hypercubical lattices and high density expansions</a>, Phys. Rev. 133 (1964) A224A239.
%H D. MacDonald, D. L. Hunter, K. Kelly and N. Jan, <a href="http://dx.doi.org/10.1088/03054470/25/6/006">Selfavoiding walks in two to five dimensions: exact enumerations and series study</a>, J Phys A: Math Gen 25 (1992) Vol. 6, 14291440 [Gives 18 terms]
%H A. M. Nemirovsky et al., <a href="http://dx.doi.org/10.1007/BF01049010">Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers</a>, J. Statist. Phys., 67 (1992), 10831108.
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/stw4d.html">Results for the 4D SelfTrapping Random Walk</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SelfAvoidingWalkConnectiveConstant.html">SelfAvoiding Walk Connective Constant</a>
%o A "brute force" FORTRAN program to count the 4D walks is available at the Pfoertner link.
%K nonn,walk,nice
%O 0,2
%A _N. J. A. Sloane_.
%E 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
%E More terms from _Hugo Pfoertner_, Dec 14 2002; Oct 19 2004
%E Further terms from _R. J. Mathar_, Aug 31 2007
