A007201 -id:A007201 - cp's OEIS frontend

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

Simon Plouffe

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

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

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.

Cf. A007201.

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

A260017 Triangle read by rows giving certain self-avoiding walk data for the triangular lattice.

Original entry on oeis.org

6, 30, 12, 138, 48, 24, 618, 180, 84, 60, 2730, 792, 264, 192, 180, 11946, 3444, 1128, 528, 552, 588

Offset: 1

N. J. A. Sloane, Jul 13 2015

See Redner (1980) for precise definition.

			Triangle begins:
6,
30,12,
138,48,24,
618,180,84,60,
2730,792,264,192,180,
11946,3444,1128,528,552,588,
...

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.

Diagonals include A001334, A007200, A007201.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions