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\title[Simplification of Two Papers of Ferri, Faccio, and D'Amico]{}
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{\Large{\bf
{Simplification of Two Papers of Ferri, Faccio, and D'Amico}
}}


{\sc Helmut Prodinger\\
Department for Algebra and Discrete Mathematics \\
TU Wien \\
Wiedner Hauptstrasse 8--10/118 \\
A-1040 Wien\\
 Austria \\
\rm email: Helmut.Prodinger@@tuwien.ac.at}
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In \cite{Paper1}, the authors come up with a ``new" numerical triangle, defined recursively by
\begin{equation}   
a_{n,k}=a_{n-1,k}+\sum_{j=0}^{n-1}a_{j,k-1},\quad n>k,\quad a_{n,n}=a_{n,0}=1~.
\end{equation}
Complicated expressions are derived for these numbers. However, they are not so ``new" at all,
since
\begin{equation}   
a_{n,k}=\binom{n+k}{n-k}~. 
\end{equation}

The second paper \cite{Paper2} is very similar; only the starting values are different:
$a_{n,0}=n+1$. 

This time we find
\begin{equation}   
a_{n,k}=\binom{n+k+1}{n-k}~. 
\end{equation}

The proofs (for instance by induction) are completely standard and therefore omitted.






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\begin{thebibliography}{1}

\bibitem{Paper1}
G.~Ferri, M.~Faccio, and A.~D'Amico.
\newblock A new numerical triangle showing links with {F}ibonacci numbers.
\newblock {\em The Fibonacci Quarterly}, 29:316--321, 1991.

\bibitem{Paper2}
G.~Ferri, M.~Faccio, and A.~D'Amico.
\newblock Fibonacci numbers and ladder network impedance.
\newblock {\em The Fibonacci Quarterly}, 30:62--67, 1992.
\end{thebibliography}



\bigskip 
\noindent 1991 \textit{Mathematics Subject Classification.}\ {05A10.}


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