Tiling Proofs of Some Fibonacci-lucas Relations
نویسنده
چکیده
We provide tiling proofs for some relations between Fibonacci and Lucas numbers, as requested by Benjamin and Quinn in their text, Proofs that Really Count. Extending our arguments yields Gibonacci generalizations of these identities.
منابع مشابه
Combinatorial Proofs of Some Identities for the Fibonacci and Lucas Numbers
We study the previously introduced bracketed tiling construction and obtain direct proofs of some identities for the Fibonacci and Lucas numbers. By adding a new type of tile we call a superdomino to this construction, we obtain combinatorial proofs of some formulas for the Fibonacci and Lucas polynomials, which we were unable to find in the literature. Special cases of these formulas occur in ...
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