%I #9 Apr 30 2024 04:13:42

%S 1,2,9,38,185,914,4706,24632,131309,708284,3861380,21225588,117511456,

%T 654474352,3664017964,20604973852,116332926949,659097637368,

%U 3745842085016,21348227213714,121974246173946,698499504058204

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

%C 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

%H Sean A. Irvine, <a href="/A057647/b057647.txt">Table of n, a(n) for n = 0..250</a>

%H C. Banderier, <a href="http://algo.inria.fr/banderier/">Analytic combinatorics of random walks and planar maps</a>, PhD Thesis, 2001.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a057/A057647.java">Java program</a> (github)

%F a(n) ~ (sqrt(3) - 1) * 2^n * 3^(n+1) / (Pi*n). - _Vaclav Kotesovec_, Apr 30 2024

%K nonn

%O 0,2

%A _Cyril Banderier_, Oct 12 2000

%E Title corrected by _Sean A. Irvine_, Jun 22 2022