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- Arthur T. Benjamin, Alex K. Eustis, Sean S. Plott
- Electr. J. Comb.
- 2008

In the book Proofs that Really Count [1], the authors use combinatorial arguments to prove many identities involving Fibonacci numbers, Lucas numbers, and their generalizations. Among these, they derive 91 of the 118 identities mentioned in Vajda’s book [2], leaving 27 identities unaccounted. Eight of these identities, presented later in this paper, have… (More)

We consider a weighted square-and-domino tiling model obtained by assigning real number weights to the cells and boundaries of an n-board. An important special case apparently arises when these weights form periodic sequences. When the weights of an nm-tiling form sequences having period m, it is shown that such a tiling may be regarded as a meta-tiling of… (More)

- Alex Eustis, Mark Shattuck
- 2011

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.… (More)

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