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\begin{center}
\vskip 1cm{\LARGE\bf Periodic Weighted Sums of \\
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Binomial Coefficients
}
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\large
Greg Dresden\\ 
Washington \& Lee University \\
Lexington, VA 24450 \\
USA\\
\href{mailto:dresdeng@wlu.edu}{\tt dresdeng@wlu.edu} \\
\ \\
Yike Li\\
Beijing City International School\\
Shuangjing, Chaoyang\\
Beijing, 100022\\ China\\
\href{redcedariver@hotmail.com}{\tt redcedariver@hotmail.com}\\ 
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\begin{abstract} 
Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Catalan numbers, Pell numbers, and more.
\end{abstract}