Pell Leonardo numbers and their matrix representations
Abstract
In this study, we investigate Pell numbers and Leonardo numbers and describe a new third-order number sequence entitled Pell Leonardo numbers. We then construct some identities, including the Binet formula, generating function, exponential generating function, Catalan, Cassini, and d’Ocagne’s identities for Pell Leonardo numbers and obtain a relation between Pell Leonardo and Pell numbers. In addition, we present some summation formulas of Pell Leonardo numbers based on Pell numbers. Finally, we create a matrix formula for Pell Leonardo numbers and obtain the determinant of the matrix.
Keywords
Leonardo numbers, Pell numbers, Binet’s formula, Generating function, Matrix representation
Ethical Statement
No approval from the Board of Ethics is required.
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