• Corpus ID: 203615646

# 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.
42 Citations

### 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.

### 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 , 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)

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

• Mathematics
Int. 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

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.