A003289 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,1).

1, 2, 4, 10, 30, 98, 328, 1140, 4040, 14542, 53060, 195624, 727790, 2728450, 10296720, 39084190, 149115456, 571504686, 2199310460, 8494701152, 32919635606, 127961125094, 498775164568, 1949112527750, 7634623480172

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• more

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

References

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

Links

• D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Crossrefs

Equals A001335(n+1) / 6 for n > 1.

Cf. A003290, A003291, A005549, A005550, A005551, A005552, A005553.

Extensions

More terms and title improved by Sean A. Irvine, Feb 13 2016

a(23)-a(24) from Bert Dobbelaere, Jan 03 2019

a(25) from Bert Dobbelaere, Jan 15 2019