A new generalization of fibonacci and lucas p-numbers

In this paper, we define a new generalization of the Fibonacci and Lucas p-numbers. Further, we build up the tree diagrams for generalized Fibonacci and Lucas p-sequence and derive the recurrence relations of these sequences by using these diagrams. Also, we show that the generalized Fibonacci and Lucas p-sequences can be reduced into the various number sequences. Finally, we develop Binet formulas for the generalized Fibonacci and Lucas p-numbers and present the numerical and graphical results, which obtained by means of the Binet formulas, for specific values of a, b and p.