Some Identities Involving the Generalized Lucas Numbers

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

Some Remarkable Identities Involving Numbers

The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers. Formulas for short multiplication are sometimes referred in English or French as remarkable identities. The same formulas could be found in works conce...

On Some Identities of k-Jacobsthal-Lucas Numbers

In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83

Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums

As in [1, 2], for rapid numerical calculations of identities pertaining to Lucas or both Fibonacci and Lucas numbers we present each identity as a binomial sum. 1. Preliminaries The two most well-known linear homogeneous recurrence relations of order two with constant coefficients are those that define Fibonacci and Lucas numbers (or Fibonacci and Lucas sequences). They are defined recursively ...