Summary: Carlitz and Riordan began a study on closed form of generating functions for powers of second-order recurrence sequences. This investigation was completed by Stănică. In this paper we consider exponential and other types of generating functions for such sequences. Moreover, an extensive table of generating functions is provided.

11B39

recurrence sequences, Fibonacci sequence, Lucas sequence, pell sequence, pell- Lucas sequence, jacobsthal sequence, jacobsthal-Lucas sequence, generating function, exponential generating function