A003291 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,1). (Formerly M1613)

2, 6, 16, 46, 140, 464, 1580, 5538, 19804, 71884, 264204, 980778, 3671652, 13843808, 52519836, 200320878, 767688176, 2954410484, 11412815256, 44237340702, 171997272012, 670612394118, 2621415708492, 10271274034254

Offset

2,1

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=2..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

Cf. A001335, A003289, A003290, A005549, A005550, A005551, A005552, A005553.

Sequence in context: A094039 A165431 A182267 * A148442 A190729 A071726

Adjacent sequences: A003288 A003289 A003290 * A003292 A003293 A003294

Keyword

nonn,walk,more

Author

N. J. A. Sloane

Extensions

More terms and title improved by Sean A. Irvine, Feb 14 2016

a(23)-a(25) from Bert Dobbelaere, Jan 15 2019

Status

approved