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A006816 Related to self-avoiding walks on square lattice.
(Formerly M4187)
2
1, 6, 29, 108, 393, 1298, 4271, 13312, 41469, 125042, 376747, 1111144, 3274475, 9505054, 27573041, 79086964, 226727667, 644301026, 1830188555, 5162408200, 14556754485, 40811281170 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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.
CROSSREFS
Sequence in context: A164274 A100874 A047923 * A184130 A326805 A061648
KEYWORD
nonn,walk
AUTHOR
EXTENSIONS
a(19)-a(22) from Sean A. Irvine, Aug 09 2017
STATUS
approved

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Last modified February 22 21:30 EST 2024. Contains 370265 sequences. (Running on oeis4.)