A057647 Number of walks of length n on the upper-right part of the hexagonal lattice.

1, 2, 9, 38, 185, 914, 4706, 24632, 131309, 708284, 3861380, 21225588, 117511456, 654474352, 3664017964, 20604973852, 116332926949, 659097637368, 3745842085016, 21348227213714, 121974246173946, 698499504058204

Offset: 0

Author

Cyril Banderier, Oct 12 2000

Keywords

• nonn

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice. - Sean A. Irvine, Jun 22 2022

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..250
• C. Banderier, Analytic combinatorics of random walks and planar maps, PhD Thesis, 2001.
• Sean A. Irvine, Java program (github)

Formula

a(n) ~ (sqrt(3) - 1) * 2^n * 3^(n+1) / (Pi*n). - Vaclav Kotesovec, Apr 30 2024

Extensions

Title corrected by Sean A. Irvine, Jun 22 2022