A174313 Number of n-step walks on hexagonal lattice (no points repeated, no adjacent points unless consecutive in path).

1, 6, 18, 54, 162, 474, 1398, 4074, 11898, 34554, 100302, 290322, 839382, 2422626, 6984342, 20110806, 57851358, 166258242, 477419658, 1369878582, 3927963138, 11255743434, 32235116502, 92267490414, 263968559874, 754837708494, 2157584748150, 6164626128066, 17606866229010

Offset: 0

Author

Joseph Myers, Nov 27 2010

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.

Fisher and Hiley give 290334 and 839466 as their last terms instead of 290322 and 839382 (see A002933). Douglas McNeil confirms the correction on the seqfan list Nov 27 2010.

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. E. Fisher and B. J. Hiley, Configuration and free energy of a polymer molecule with solvent interaction, J. Chem. Phys., 34 (1961), 1253-1267.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Crossrefs

Cf. A173380 for square lattice equivalent.

Extensions

a(19)-a(28) from Bert Dobbelaere, Jan 02 2019