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A118313 Sum of squared end-to-end distances of all n-step self-avoiding walks on the simple cubic lattice. 4


%S 0,6,72,582,4032,25566,153528,886926,4983456,27401502,148157880,

%T 790096950,4166321184,21760624254,112743796632,580052260230,

%U 2966294589312,15087996161382,76384144381272,385066579325550,1933885653380544,9679153967272734,48295148145655224,240292643254616694,1192504522283625600,5904015201226909614,29166829902019914840,143797743705453990030,707626784073985438752,3476154136334368955958,17048697241184582716248,83487969681726067169454,408264709609407519880320,1993794711631386183977574,9724709261537887936102872,47376158929939177384568598,230547785968352575619933376

%N Sum of squared end-to-end distances of all n-step self-avoiding walks on the simple cubic lattice.

%C Number of walks is A001412(n).

%C a(5) is 25556 according to MacDonald et al., but 25566 according to Clisby et al. and is therefore conjectural for now. - _R. J. Mathar_, Aug 31 2007

%C Confirmed that a(5) is 25566 [from Nathan Clisby].Right-hand column, table, p.5 of Schram.

%H R. D. Schram, G. T. Barkema, R. H. Bisseling, <a href="/A118313/b118313.txt">Table of n, a(n) for n = 0..36</a>

%H N. Clisby, R. Liang and G. Slade <a href="http://dx.doi.org/10.1088/1751-8113/40/36/003">Self-avoiding walk enumeration via the lace expansion</a> J. Phys. A: Math. Theor. vol. 40 (2007) p 10973-11017, Table A5 for n<=30.

%H A. J. Guttmann, <a href="http://dx.doi.org/10.1088/0305-4470/20/7/029">On the critical behavior of self-avoiding walks</a>, J. Phys. A 20 (1987), 1839-1854.

%H D. MacDonald, S. Joseph, D. L. Hunter, L. L. Mosley, N. Jan and A. J. Guttmann, <a href="http://dx.doi.org/10.1088/0305-4470/33/34/303">Self-avoiding walks on the simple cubic lattice</a>,J Phys A: Math Gen 33 (2000) No 34, 5973-5983

%H Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling, <a href="http://dx.doi.org/10.1088/1742-5468/2011/06/P06019">Exact enumeration of self-avoiding walks</a>, J Stat. Mech. (2011) P06019.

%Y Cf. A001412, A078605, A079156.

%K nonn

%O 0,2

%A _R. J. Mathar_, May 14 2006

%E a(5) corrected by _Nathan Clisby_, Nov 24 2010

%E a(14), a(22) corrected by _Hugo Pfoertner_, Aug 13 2011

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Last modified March 30 15:20 EDT 2020. Contains 333126 sequences. (Running on oeis4.)