Sunday, February 14, 2016

Analogues of a Fibonacci-Lucas Identity

Recently, in 2014, Sury published a Fibonacci-Lucas  identity in the Monthly. It turned out that the identity had appeared earlier (as Identity 236 in Benjamin and Quinn's book: Proofs that count: The art of combinatorial proof). When I tried to prove it using my usual telescoping method, I found its connection with one of the oldest Fibonacci identities due to Lucas in 1876. I also found many generalizations and analogous identities for other Fibonacci type sequences and polynomials. This  small paper has been accepted in the Fibonacci Quarterly.

Here is a link to a preprint: Analogues of a Fibonacci-Lucas Identity

Update: Its has appeared. The ref is: Analogues of a Fibonacci-Lucas identity, Fibonacci Quart., 54 (no. 2) 166-171,  (2016)

I use the approach of my earlier paper on Telescoping: In praise of an elementary identity of Euler.

I am pleased, because I have thought of getting a paper in the Fibonacci Quarterly since I was in high school, and feel lucky I found something they found acceptable!