On Pell and Pell-Lucas numbers

Abstract

In this work, we consider the linear recurrent sequences with constant coefficients of order 2, focusing on those defining Pell and Pell-Lucas numbers. In this context, we have examined the corresponding Binet formulas and the possibilities for a Pell or Pell-Lucas number to become a member of another family such as the families of triangular, pentagonal, heptagonal numbers, ... . We also reviewed some identities linking these numbers, and finished our work with some formulas involving the sum and multiplication of these numbers.