Some identities for generalized Fibonacci and Lucas numbers

Some Identities for Generalized Fibonacci and Lucas Sequences

In this study, we define a generalization of Lucas sequence {pn}. Then we obtain Binet formula of sequence {pn} . Also, we investigate relationships between generalized Fibonacci and Lucas sequences.

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 √

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

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 ...

New Sums Identities In Weighted Catalan Triangle With The Powers Of Generalized Fibonacci And Lucas Numbers

In this paper, we consider a generalized Catalan triangle de…ned by km n 2n n k for positive integer m: Then we compute the weighted half binomial sums with the certain powers of generalized Fibonacci and Lucas numbers of the form n X k=0 2n n+ k km n X tk; where Xn either generalized Fibonacci or Lucas numbers, t and r are integers for 1 m 6: After we describe a general methodology to show how...