A007200 Number of self-avoiding walks on hexagonal lattice, with additional constraints.

12, 48, 180, 792, 3444, 15000, 64932, 280200, 1204572, 5159448, 22043292, 93952428, 399711348, 1697721852, 7200873444, 30500477676, 129049335924, 545436439536, 2303305856916

Offset: 2

Author

Simon Plouffe

Keywords

• nonn
• walk

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

• 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.

Extensions

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