%PRIMA TAVOLA DEI 3 MOTIVI
\section{Tables}\label{tables}
\begin{table}[!h]
\begin{center}
\begin{tabular}{|c|c|c|}
symmetry class & avoided patterns & enumerating sequence\\
\hline \hline

N1&\{1-23,2-13,3-12\}&\\
%\hline
N2&\{1-23,2-13,31-2\}&\\
%\hline
N3&\{1-23,21-3,3-12\}&\\
%\hline
N4&\{1-23,21-3,31-2\}&\\
%\hline
N5&\{12-3,3-12,2-13\}&\\
%\hline
N6&\{12-3,3-12,21-3\}&\\
%\hline
N7&\{12-3,31-2,2-13\}&\\
%\hline
N8&\{12-3,31-2,21-3\}&\\
%\hline
N9&\{1-23,2-13,2-31\}&\\
%\hline
N10&\{1-23,2-13,23-1\}&\\
%\hline
N11&\{1-23,21-3,2-31\}&\\
%\hline
N12&\{1-23,21-3,23-1\}&\\
%\hline
N13&\{2-13,2-31,1-32\}& $\{n\}_{n\geq 1}$\\
%\hline
N14&\{2-13,23-1,1-32\}&\\
%\hline
N15&\{2-13,2-31,13-2\}&\\
%\hline
N16&\{2-13,23-1,13-2\}&\\
%\hline
N17&\{2-31,21-3,13-2\}&\\
%\hline
N18&\{2-31,21-3,1-32\}&\\
%\hline
N19&\{13-2,21-3,23-1\}&\\
%\hline
N20&\{21-3,23-1,1-32\}&\\
%\hline
N21&\{1-23,2-31,31-2\}&\\
%\hline
N22&\{1-23,23-1,31-2\}&\\
%\hline
N23&\{1-23,2-31,3-12\}&\\
%\hline
N24&\{1-23,1-32,3-21\}&\\
\hline
A1&\{1-23,12-3,23-1\}&\\
A2&\{2-31,23-1,1-32\}&\\
A3&\{2-31,23-1,13-2\}&\\
A4&\{1-23,12-3,2-13\}&\\
A5&\{1-23,2-13,21-3\}&$\{2^{n-1}\}_{n\geq 1}$\\
A6&\{1-23,3-12,31-2\}&\\
A7&\{31-2,3-12,13-2\}&\\
A8&\{31-2,3-12,1-32\}&\\
A9&\{2-13,21-3,1-32\}&\\
A10&\{2-13,21-3,13-2\}&\\
\hline
A11&\{1-23,23-1,3-12\}&$\{2{n-2}+1\}_{n\geq 1}$\\
\hline
\end{tabular}
\end{center}
\caption{permutations avoiding three patterns}\label{3mot1}
\end{table}
