Some combinatorial identities via Fibonacci numbers

Some Identities for Fibonacci and Incomplete Fibonacci p-Numbers via the Symmetric Matrix Method

We obtain some new formulas for the Fibonacci and Lucas p-numbers, by using the symmetric infinite matrix method. We also give some results for the Fibonacci and Lucas p-numbers by means of the binomial inverse pairing.

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 ...

Some Trigonometric Identities Involving Fibonacci and Lucas Numbers

In this paper, using the number of spanning trees in some classes of graphs, we prove the identities: Fn = 2n−1 n √

Generalizations of Some Identities Involving the Fibonacci Numbers

Fibonacci numbers and trigonometric identities

Webb & Parberry proved in 1969 a startling trigonometric identity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.