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

0, 6, 72, 582, 4032, 25566, 153528, 886926, 4983456, 27401502, 148157880, 790096950, 4166321184, 21760624254, 112743796632, 580052260230, 2966294589312, 15087996161382, 76384144381272, 385066579325550, 1933885653380544, 9679153967272734, 48295148145655224, 240292643254616694, 1192504522283625600, 5904015201226909614, 29166829902019914840, 143797743705453990030, 707626784073985438752, 3476154136334368955958, 17048697241184582716248, 83487969681726067169454, 408264709609407519880320, 1993794711631386183977574, 9724709261537887936102872, 47376158929939177384568598, 230547785968352575619933376

Offset: 0

Author

R. J. Mathar, May 14 2006

Keywords

• nonn

Comments

Number of walks is A001412(n).

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

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

Links

• R. D. Schram, G. T. Barkema, R. H. Bisseling, Table of n, a(n) for n = 0..36
• 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 A5 for n<=30.
• A. J. Guttmann, On the critical behavior of self-avoiding walks, J. Phys. A 20 (1987), 1839-1854.
• D. MacDonald, S. Joseph, D. L. Hunter, L. L. Mosley, N. Jan and A. J. Guttmann, Self-avoiding walks on the simple cubic lattice,J Phys A: Math Gen 33 (2000) No 34, 5973-5983
• Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling, Exact enumeration of self-avoiding walks, J Stat. Mech. (2011) P06019.

Crossrefs

Cf. A001412, A078605, A079156.

Extensions

a(5) corrected by Nathan Clisby, Nov 24 2010

a(14), a(22) corrected by Hugo Pfoertner, Aug 13 2011