In this paper, we consider the usual Lucas numbers and the generalized order-k Fibonacci numbers. Then we give a new definition for generalization of the Lucas numbers. Therefore, we give the ...

In this paper, we study the symmetric and the generating functions for odd and even terms of the second-order linear recurrence sequences. we introduce a operator in order to derive a new family of ...

An unusual arrangement of leaves in a 407-million-year-old fossilized plant is complicating scientists’ understanding of plant evolution. Most land plants living today have spiral patterns involving ...

Tenacity has taken a roadblock and turned it into a possible route to the development of quantum computing. Long before Dr. Jukka Vayrynen was an assistant professor at the Purdue Department of ...