Octave recurrence relations
Odometers and systems of numeration
On a class of combinatorial Diophantine equations.
On a class of polynomials with integer coefficients.
On a conjecture concerning sequences of the third order
On a conjecture of Morgan Ward, I
On a conjecture of Morgan Ward, II
On a conjecture of Morgan Ward, III
On a family of generalized Pascal triangles defined by exponential Riordan arrays.
On a generalization of duality triads
Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.
On a generalization of the Narayana triangle.
On a generalization of the Pell sequence
The Pell sequence is the second order linear recurrence defined by with initial conditions and . In this paper, we investigate a generalization of the Pell sequence called the -generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced....
On a new family of generalized Stirling and Bell numbers.
On a one-parameter family of Riordan arrays and the weight distribution of MDS codes.
On a problem of Erdős and Graham concerning digits
On a sequence arising in algebraic geometry.
On a simultaneous approximation problem concerning binary recurrences.
On a strange recursion of Golomb.
On Balancing and Lucas-balancing Quaternions
The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
On binomial sums for the general second order linear recurrence.