A007200 Number of self-avoiding walks on hexagonal lattice, with additional constraints. (Formerly M4838)

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

Table of n, a(n) for n=2..20.

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

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

Adjacent sequences: A007197 A007198 A007199 * A007201 A007202 A007203

Keyword

nonn,walk

Author

Simon Plouffe

Extensions

a(15)-a(20) from Sean A. Irvine, Nov 20 2017

Status

approved