login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A007200
Number of self-avoiding walks on hexagonal lattice, with additional constraints.
(Formerly M4838)
2
12, 48, 180, 792, 3444, 15000, 64932, 280200, 1204572, 5159448, 22043292, 93952428, 399711348, 1697721852, 7200873444, 30500477676, 129049335924, 545436439536, 2303305856916
OFFSET
2,1
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
The extra constraint here is that the next to "middle" points of the walk must be adjacent in the lattice. Exact details are in the Redner paper. - Sean A. Irvine, Nov 20 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
S. Redner, Distribution functions in the interior of polymer chains, J. Phys. A 13 (1980), 3525-3541, doi:10.1088/0305-4470/13/11/023.
CROSSREFS
Cf. A007201.
Sequence in context: A190622 A117027 A161171 * A061148 A339760 A221908
KEYWORD
nonn,walk
AUTHOR
EXTENSIONS
a(15)-a(20) from Sean A. Irvine, Nov 20 2017
STATUS
approved