Related papers: Generalized Balancing and Balancing-Lucas numbers
In this paper, we introduce relations between binomial sums involving (generalized) Fibonacci and Lucas numbers, and different kinds of binomial coefficients. We also present some relations between sums with two and three binomial…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
I present all the details in calculating the posterior distribution of the conjugate Normal-Gamma prior in Bayesian Linear Models (BLM), including correlated observations, prediction, model selection and comments on efficient numeric…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.
This paper summarizes our latest understanding and results about the application of the Mathematics Of Enumeration to Tanner Graphs that have a regular structure called Balanced Tanner Graphs. Some preliminaries of permutation groups have…
Let $B_n$ be the $n$-th balancing number. In this paper, we give some explicit expressions of $\sum_{l=0}^{2 r-3}(-1)^l\binom{2 r-3}{l}\sum_{j_1+\cdots+j_r=n-2 l\atop j_1,\dots,j_r\ge 1}B_{j_1}\cdots B_{j_r}$ and…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.
In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy's integral formula in the…
We derive generalizations of a couple of inverse tangent summation identities involving Fibonacci and Lucas numbers. As byproducts we establish many new inverse tangent identities involving the Fibonacci and Lucas numbers.
A novel power series representation of the generalized Marcum $Q-$function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a…
In this letter we make a brief review of some basic properties (the matrix elements, the trace, the Glauber formula) of coherent operators and study the corresponding ones for generalized coherent operators based on Lie algebra su(1,1). We…
In this paper, we propose a generalization of a congruence due to Carlitz.
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…
We present here a more general version of the balanced pair algorithm. This version works in the reducible case and terminates more often than the standard algorithm. We present examples to illustrate this point. Lastly, we discuss the…
This paper presents new identities expressing the terms of Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices through powers of Lucas numbers and binomial coefficients. The obtained formulas rely on the application…
We present determinantal representations of the Catalan numbers, k-Fuss-Catalan numbers, and its generalized number. The entries of the normalized Hessenberg matrices are the binomial coefficients that related with the enumeration of…