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

0,2

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.

Sequence in context: A334327 A129532 A151719 * A283095 A281774 A036292

Adjacent sequences: A118310 A118311 A118312 * A118314 A118315 A118316

Keyword

nonn

Author

R. J. Mathar, May 14 2006

Extensions

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

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

Status

approved