Related papers: New binomial Fibonacci sums
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
This paper presents both a method and a result. The result presents a closed formula for the sum of the first $m+1,m \ge 0,$ squares of the sequence $F^{(k)}$ where each member is the sum of the previous $k$ members and with initial…
In this study, we apply "r" times the binomial transform to k-Lucas sequence. Also, the Binet formula, summation, generating function of this transform are found using recurrence relation. Finally, we give the properties of iterated…
In this work, we defined neo balcobalancing numbers, neo Lucas-balcobalancing numbers, neo balcobalancers and neo Lucas-balcobalancers and derived the general terms of these numbers in terms of balancing numbers. Conversely we deduced the…
In this paper, we find the closed sums of certain type of Fibonacci related convergent series. In particular, we generalize some results already obtained by Brousseau, Popov, Rabinowitz and others.
In this paper, some $k$-Fibonacci and $k$-Lucas with arithmetic indexes sums are derived by using the matrices $R_{a}=\left[ \begin{array}{lr} L_{k,a} & -(-1)^{a} \\ 1 & 0 \end{array}\right]$ and $S_{a}=\frac{1}{2}\left[ \begin{array}{lr}…
We establish some identities relating two sequences that are, as explained, related to the Tribonacci sequence. One of these sequences bears the same resemblance to the Tribonacci sequence as the Lucas sequence does to the Fibonacci…
In this paper we give new identities involving q-Euler polynomials of higher order.
In this paper, we introduce h(x)-Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K (K = R,C), which generalize both h(x)-Fibonacci quaternion polynomials and h(x)-Fibonacci octonion polynomials. For…
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
In this work, by using Pauli matrices, we introduce four families of polynomials indexed over the positive integers. These polynomials have rational or imaginary rational coefficients. It turns out that two of these families are closely…
The moments of the Lucas polynomials and of the Chebyshev polynomials of the first kind are (multiples of) central binomial coefficients and the moments of the Fibonacci polynomials and of the Chebyshev polynomials of the second kind are…
In this paper we establish two symmetric identities on sums of products of Euler polynomials.
In 2016, Y\"uce and Torunbalc\i\ Ayd\i n \cite{Yuc-Tor} defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the…
Two well-known $q$-Hermite polynomials are the continuous and discrete $q$-Hermite polynomials. In this paper we consider a new family of $q$-Hermite polynomials and prove several curious properties about these polynomials. One striking…