# THE FIBONACCI QUARTERLY

@inproceedings{Quarterly2010THEFQ, title={THE FIBONACCI QUARTERLY}, author={Fibonacci Quarterly}, year={2010} }

. By interpreting various sums involving Fibonacci and Lucas numbers physically, we show how one can often generate an additional summation with little eﬀort. To illustrate the fruitfulness of the approach, we establish some elegant summations that we believe are new.

## Figures from this paper

## 42 Citations

### Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums

- Mathematics
- 2012

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.

### FIBONACCI AND LUCAS REPRESENTATIONS

- Mathematics
- 2016

An identity which relates the Fibonacci and Lucas representations of integers to the Riemann zeta function is derived.

### Generalized Fibonacci-Like Polynomial and its Determinantal Identities

- Mathematics
- 2012

It is well known that the Fibonacci polynomials are of great importance in the study of many subjects such as Algebra, geometry, combinatorics and number theory itself. Fibonacci polynomials defined…

### Fibonacci Identities as Binomial Sums II

- Mathematics
- 2012

As in [2], our goal in this article is to write some more prominent and fundamental identities regarding Fibonacci numbers as binomial sums.

### A SMOOTH TIGHT UPPER BOUND FOR THE FIBONACCI REPRESENTATION FUNCTION R(N)

- Mathematics
- 2009

The function R(n) that counts the number of representations of the integer n as the sum of distinct Fibonacci numbers has been studied for over 40 years, and many fascinating properties have been…

### The q-Pilbert matrix

- MathematicsInt. J. Comput. Math.
- 2012

A generalized Filbert matrix is introduced, sharing properties of the Hilbert matrix and Fibonacci numbers. Explicit formulae are derived for the LU-decomposition and their inverses, as well as the…

### COMBINATORIAL PROOFS OF SOME FORMULAS FOR Lm

- Mathematics, Computer Science
- 2010

This paper provides combinatorial proofs of some formulas for the power of a Lucas number which as far as the authors know have only been proven using other methods using a new kind of object called a bracket into the usual square-and-domino tiling model.

### Asymptotic Behavior of Gaps Between Roots of Weighted Factorials

- Mathematics
- 2014

Abstract : Abstract. Here, we find a general method for computing the limit of differences of consecutive terms of n-th roots of weighted factorials by a sequence xn (under some technical condition).

### SOME CONGRUENCES INVOLVING EULER NUMBERS

- Mathematics
- 2009

In this paper, we obtain some explicit congruences for Euler numbers modulo an odd prime power in an elementary way. The classical Bernoulli polynomials Bn(x) and Euler polynomials En(x) are usually…

### Some Formulae of Genocchi Polynomials of Higher Order

- Mathematics
- 2020

In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.

## References

SHOWING 1-10 OF 2,149 REFERENCES

### On the Matrix Approach to Fibonacci Numbers and the Fibonacci Pseudoprimes.

- Mathematics
- 1977

Abstract : A study of those integers n such that L sub n = 1 (mod n), where I sub n are the Lucas numbers. (Author)

### Polynomial Generalizations of the Pell sequence and the Fibonacci sequence

- Mathematics
- 2002

We provide three new polynomial generalizations for the Pell sequence an, also, new formulas for this sequence. An interesting relation, in terms of partitions, between the Pell and the Fibonacci…

### On Fibonacci-Hessenberg matrices and the Pell and Perrin numbers

- MathematicsAppl. Math. Comput.
- 2012

### Formulas for Fibonomial sums with generalized Fibonacci and Lucas coefficients

- Mathematics
- 2011

We consider certain Fibonomial sums with generalized Fibonacci and Lucas numbers coefficients and compute them explicitly. Some corollaries are also presented. The technique is to rewrite everything…

### A PROOF OF A CONJECTURE OF MELHAM

- Mathematics
- 2010

In this paper, we consider Melham's conjecture involving Fibonacci and Lucas numbers. After rewriting it in terms of Fibonomial coefficients, we give a solution of the conjecture by evaluating a…

### Some Properties of the Fibonacci Numbers

- Mathematics
- 1967

This thesis is presented as an introduction to the Fibonacci sequence of integers. It is hoped that this thesis will create in the reader more interest in this type of sequence and especially the…

### Families of fibonacci and lucas sums via the moments of a random variable

- Mathematics
- 2011

Abstract. In this paper we show how the expectation of a particular random variable gives rise to an infinite series whose coefficients are certain functions of the Fibonacci numbers. A general…

### FIBONACCI-RIESEL AND FIBONACCI-SIERPI ¶ NSKI NUMBERS

- Mathematics
- 1962

Here, we prove that there are inflnitely many Fibonacci numbers which are Riesel numbers. We also show that there are inflnitely many Fibonacci numbers which are Sierpinski numbers.