\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Definitions and fundamental results about trees}{}% 2
\BOOKMARK [2][-]{subsection.2.1}{The tree T}{section.2}% 3
\BOOKMARK [2][-]{subsection.2.2}{Shortest walks in T}{section.2}% 4
\BOOKMARK [2][-]{subsection.2.3}{The tree R}{section.2}% 5
\BOOKMARK [2][-]{subsection.2.4}{Projection of walks of T into walks of R}{section.2}% 6
\BOOKMARK [1][-]{section.3}{Proof of Theorem 1}{}% 7
\BOOKMARK [2][-]{subsection.3.1}{Step 1: the growth rate of n\(a,b\) does not depend on \(a,b\)}{section.3}% 8
\BOOKMARK [2][-]{subsection.3.2}{Step 2: an explicit expression of n\(a,b\) in terms of k\(|b-a|,a\) for \(a,b\)=\(1,\) or \(1,-1\)}{section.3}% 9
\BOOKMARK [2][-]{subsection.3.3}{Step 3: an explicit expression of the growth rate of S\(n\(1,\)\) and S\(n\(1,-1\)\)}{section.3}% 10
\BOOKMARK [2][-]{subsection.3.4}{Step 4: growth rate of S\(n\(a,b\)\) for all pairs \(a,b\)}{section.3}% 11
\BOOKMARK [1][-]{section.4}{Interesting properties of R and related trees}{}% 12
\BOOKMARK [2][-]{subsection.4.1}{Values in the n-th row of R}{section.4}% 13
\BOOKMARK [2][-]{subsection.4.2}{Positions of 0-nodes in T}{section.4}% 14
\BOOKMARK [2][-]{subsection.4.3}{The matrix point of view}{section.4}% 15
\BOOKMARK [2][-]{subsection.4.4}{Size of walks in R}{section.4}% 16
\BOOKMARK [1][-]{section.5}{Some perspectives}{}% 17
\BOOKMARK [1][-]{section.6}{Acknowledgments}{}% 18