Pell Coding and Pell Decoding Methods with Some Applications

We develop a new coding and decoding method using the generalized Pell $(p,i)$-numbers for $p=1$. The relations among the code matrix elements, error detection, and correction have been established for coding theory when $p=i=1$. We give two new blocking algorithms using Pell numbers and generalized Pell $(p,i)$-numbers for $p=1$

The Binet formula, sums and representations of generalized Fibonacci p-numbers

AbstractIn this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers