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Full-Text Articles in Physical Sciences and Mathematics
A Study On Horadam Hybrid Numbers, Tuncay Deni̇z Şentürk, Göksal Bi̇lgi̇ci̇, Ahmet Daşdemi̇r, Zafer Ünal
A Study On Horadam Hybrid Numbers, Tuncay Deni̇z Şentürk, Göksal Bi̇lgi̇ci̇, Ahmet Daşdemi̇r, Zafer Ünal
Turkish Journal of Mathematics
In this paper, we study Horadam hybrid numbers. For these numbers, we give the exponential generating function, Poisson generating function, generating matrix, Vajda's, Catalan's, Cassini's, and d'Ocagne's identities. In addition, we offer Honsberger formula, general bilinear formula, and some summation formulas for these numbers.
Some Higher-Order Identities For Generalized Bi-Periodic Horadam Sequences, Ho-Hon Leung, Eli̇f Tan
Some Higher-Order Identities For Generalized Bi-Periodic Horadam Sequences, Ho-Hon Leung, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.