\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Arthur T. Benjamin, Alex K. Eustis, and Sean S. Plott}
%
%
\medskip
\noindent
%
%
{\bf The 99th Fibonacci Identity}
%
%
\vskip 5mm
\noindent
%
%
%
%
We provide elementary combinatorial proofs of several Fibonacci and
Lucas number identities left open in the book {\it Proofs That
Really Count} [1], and generalize these to Gibonacci sequences $G_n$
that satisfy the Fibonacci recurrence, but with arbitrary real
initial conditions. We offer several new identities as well. Among
these, we prove $\sum_{k\geq 0}{n \choose k}G_{2k} = 5^n G_{2n}$ and
$\sum_{k\geq 0}{n \choose k}G_{qk}(F_{q-2})^{n-k} = (F_q)^n G_{2n}$.

\bye

.
