On the Third-Order Horadam and Geometric Mean Sequences

On the Jacobsthal, Horadam and Geometric Mean Sequences

This paper, in considering aspects of the geometric mean sequence, offers new results connecting Jacobsthal and Horadam numbers which are established and then proved independently.

On some properties and applications of Horadam sequences

The Horadam sequence is a generalization of the Fibonacci numbers in the complex plane, depending on a family of four complex parameters: two recurrence coefficients and two initial conditions. The necessary and sufficient periodicity conditions formulated in [1] are used to enumerate all Horadam sequences with a given period [2]. The geometry of periodic orbits is analyzed, where regular star-...

On the Characterization of Periodic Generalized Horadam Sequences

The Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrix-based method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are genera...

On Third Geometric-Arithmetic Index of Graphs

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.

Estimation of Third - Order Correlationswithin Mean Field