A006814 -id:A006814 - cp's OEIS frontend

A006815 Related to self-avoiding walks on square lattice.

1, 6, 23, 84, 283, 930, 2921, 9096, 27507, 82930, 244819, 722116, 2096603, 6087290, 17458887, 50090544, 142317089, 404543142

Offset: 1

N. J. A. Sloane

After constructing a self-avoiding walk, bridge together all adjacent neighboring sites on the walk. a(n) is the sum of the lengths of the shortest path in each of the resulting structures from beginning to end (i.e., using the original path and any bridges), across all walks of length n. My attempt to compute this sequence diverges from the listed terms at n=9, for which I get a(9)=27511, a(10)=82938, .... - Sean A. Irvine, Aug 09 2017

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. S. Manna, A. J. Guttmann and A. K. Roy, Diffusion on self-avoiding walk networks, J. Phys. A 22 (1989), 3621-3627.

Cf. A006814, A006816.

A006816 Related to self-avoiding walks on square lattice.

Original entry on oeis.org

1, 6, 29, 108, 393, 1298, 4271, 13312, 41469, 125042, 376747, 1111144, 3274475, 9505054, 27573041, 79086964, 226727667, 644301026, 1830188555, 5162408200, 14556754485, 40811281170

Offset: 1

N. J. A. Sloane

After constructing a self-avoiding walk, bridge together all adjacent neighboring sites on the walk. This sequence is sum of the total number of links after adding bridges across all walks of length n. - Sean A. Irvine, Aug 09 2017

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. J. Guttmann and J. Wang, The extension of self-avoiding random walk series in 2 dimensions, Preprint. (Annotated scanned copy)
B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, Tables and references for self-avoiding walks counts [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The self-avoiding walk"]
S. S. Manna, A. J. Guttmann and A. K. Roy, Diffusion on self-avoiding walk networks, J. Phys. A 22 (1989), 3621-3627.

Cf. A001411, A006814, A006815.

a(19)-a(22) from Sean A. Irvine, Aug 09 2017

cp's OEIS Frontend

A006815 Related to self-avoiding walks on square lattice.

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