Benjamin, Arthur T.; Eustis, Alex K.; Plott, Sean S.

The 99th Fibonacci identity

Electron. J. Comb. 15(1), Research Paper R34, 13 p. (2008)


Summary: We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left open in the book Proofs That Really Count [1], 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. Among these, we prove n G n G k$\geq 0$ k 2k = 5nG2n and k$\geq 0$ k qk (Fq - 2)n - k = (Fq )nG2n.

Mathematics Subject Classification

05A19, 11B39