We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left open in the book Proofs That Really Count , and generalize these to Gibonacci sequences Gn that satisfy the Fibonacci recurrence, but with arbitrary real initial conditions. We offer several new identities as well.
 A. T. Benjamin and J. J. Quinn, Proofs That Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions, 27, Mathematical Association of America, Washington, DC, 2003
© 2008 The Electronic Journal of Combinatorics
Benjamin, Arthur, Alex Eustis, and Sean Plott. "The 99th Fibonacci Identity." The Electronic Journal of Combinatorics 15.1 (2008).
Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,452.
First published in the Electronic Journal of Combinatorics, vol. 15, no. 1 (2008).
Publisher pdf, posted with permission.