A003289 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,1). (Formerly M1229)

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

1,2

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

Table of n, a(n) for n=1..25.

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.

Sequence in context: A362637 A149835 A149836 * A087161 A372018 A360814

Adjacent sequences: A003286 A003287 A003288 * A003290 A003291 A003292

Keyword

nonn,walk,more

Author

N. J. A. Sloane

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

Status

approved