Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums
نویسندگان
چکیده
As in [1, 2], for rapid numerical calculations of identities pertaining to Lucas or both Fibonacci and Lucas numbers we present each identity as a binomial sum. 1. Preliminaries The two most well-known linear homogeneous recurrence relations of order two with constant coefficients are those that define Fibonacci and Lucas numbers (or Fibonacci and Lucas sequences). They are defined recursively as We note that aside from the boundary conditions, Fibonacci and Lucas numbers are represented by the same recurrence relation. This is the reason that Fibonacci and Lucas numbers have so many common or very similar properties. For example, the ratio of two consecutive Fibonacci numbers as well
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