Some identities of the k-Pell-Lucas sequence and their relationship to the Modified k-Pell sequence allow us to obtain some identities for Modified k-Pell numbers. Also the ordinary generating function for the Modified k-Pell sequence and another expression for the general term of the sequence, using the ordinary generating function, is provided. Mathematics Subject Classification 2010: 11B37, ...

In this study, we present the Catalan transforms of k-Pell sequence, k-Pell–Lucas sequence and Modified examine properties sequences. Then apply Hankel transform to sequence. Also, obtain generating functions Furthermore, acquire an interesting characteristic related determinant

In this paper we consider the k-Pell numbers sequence and present some properties involving the k-Pell numbers. The theoretical basis of using generating matrices for deriving the explicit formula for the term of order n of the k-Pell numbers sequence and also to get the well-known Cassini’s identity using linear algebra. Mathematics Subject Classification: 11B37, 05A15, 11B83.

We obtain the Binet’s formula for k-Pell numbers and as a consequence we get some properties for k-Pell numbers. Also we give the generating function for k-Pell sequences and another expression for the general term of the sequence, using the ordinary generating function, is provided. Mathematics Subject Classification: 11B37, 05A15, 11B83.

We obtain the Binet’s formula for k-Pell-Lucas numbers and as a consequence we obtain some properties for k-Pell-Lucas numbers. Also we give the generating function for the k-Pell-Lucas sequences and another expression for the general term of the sequence, using the ordinary generating function, is provided. Mathematics Subject Classification: 11B37, 05A15, 11B83.

We provide three new polynomial generalizations for the Pell sequence an, also, new formulas for this sequence. An interesting relation, in terms of partitions, between the Pell and the Fibonacci sequences is given, Finally two combinatorial interpretations for the Fibonacci numbers are given by making use of the Rogers-Ramanujan identities.

We use a diagonal matrix for getting the Binet’s formula for k-Pell sequence Also the n power of the generating matrix for k-Pell-Lucas sequence is established and basic properties involving the determinant allow us to obtain its Cassini’s identity. Mathematics Subject Classification: 11B37, 05A15, 11B83.