A new member of the Pell sequences: the pseudo-Pell sequence

In this study, we define a new family of the Pell numbers and establish some properties of the relation to the ordinary Pell numbers. We give some identities the pseudo-Pell numbers. Moreover, we obtain the Binet’s formula, generating function formula and some formulas for this new type numbers. Morever, we give the matrix representation of the pseudo-Pell numbers.