SOME IDENTITIES FOR SEQUENCES OF BINOMIAL SUMS OF GENERALIZED PADOVAN IDENTITIES INCLUDING POWERS AND BINOMIAL COEFFICIENTS

Dişkaya, Orhan

In this work, we investigate several identities of the generalized Padovan sequence, including binomial coefficients, using the method of ordinary power series generat- ing functions. We explore the characteristics and identities of generalized Padovan sequences, examining binomial coefficients and other extended identities through this method. Nevertheless, specific cases of third-order sequences have been ex- plored and applied in this context. By employing various techniques, we aim to derive new results concerning third-order recurrence relations, enhancing our com- prehension of these complex sequences.