Matrix methods are extremely useful for deriving some well-known Fibonacci properties such as Cassini identity, d’Ocagne identity, and the convolution property. In this work, a particular matrix was defined, such as the matrix used by Mc Laughlin [11]. Using this new matrix, some well-known important and fundamental properties of generalized Fibonacci-like sequences are given. Later, many identities containing the elements of these sequences were obtained through the proposed matrix. Moreover, some equations obtained in this study have not been studied in the literature. The use of the matrix discussed here can be used to generalize some of the work that has been done to find significant identities.

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Some Identities for Horadam Numbers by the Matrix Methods

  • Serpil Halici

摘要

Matrix methods are extremely useful for deriving some well-known Fibonacci properties such as Cassini identity, d’Ocagne identity, and the convolution property. In this work, a particular matrix was defined, such as the matrix used by Mc Laughlin [11]. Using this new matrix, some well-known important and fundamental properties of generalized Fibonacci-like sequences are given. Later, many identities containing the elements of these sequences were obtained through the proposed matrix. Moreover, some equations obtained in this study have not been studied in the literature. The use of the matrix discussed here can be used to generalize some of the work that has been done to find significant identities.