As their results began to crystallize, at first they didn’t notice the striking patterns emerging. But a colleague who reviewed their work spotted the famed Fibonacci numbers—a list whose entries have ...

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 ...

Pine cones. Stock-market quotations. Sunflowers. Classical architecture. Reproduction of bees. Roman poetry. What do they have in common? In one way or another, these and many more creations of nature ...