Recently generalized Fibonacci numbers have received increasing attention. Some properties that are well known for traditional Fibonacci numbers do not generalize easily, some others do not generalize at all. In this paper we report some properties that we have generalized. Section 1 introduces the notation and a theorem due to...
We investigate several methods of computing Fibonacci numbers quickly and generalize some properties of the Fibonacci numbers to degree r Fibonacci (R-nacci) numbers. Sections 2 and 3 present several algorithms for computing the traditional, degree two, Fibonacci numbers quickly. Sections 4 and 5 investigate the structure of the binary representation...