Summary
The convolution of the Fibonacci numbers and the Lucas numbers is equal to a simple multiple of a Fibonacci number. We show how this can be generalized to other Fibonacci-type and Lucas-type numbers. Along the way, we discuss generating functions and Newton’s Identities.
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Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Greg Dresden
Greg Dresden (MR Author ID: 623871) received his Ph.D. from the University of Texas in 1997 and now teaches at Washington and Lee University in the Blue Ridge Mountains of Virginia. When not thinking about math, he enjoys playing piano and spending time with family. As a living kidney donor, he advocates for everyone to learn more about living organ donation.
Yichen Wang
Yichen Wang (MR Author ID: 1440799) is a freshman at UCLA working toward a B.S. degree in Applied Mathematics. He plans to dig deeper into the application of mathematics and programming in financial engineering in the future. In his free time, he enjoys writing Chinese calligraphy, playing the piano, and reading science fiction novels with cats.