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Combinatorialization of Sury and McLaughlin identities, general linear recurrences in a unified approach (2009.06162v1)
Published 14 Sep 2020 in math.CO
Abstract: In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix. Also, we derive a determinantal expression of Fibonacci and Lucas numbers. We prove Binets formula for Fibonacci and Lucas numbers in a purely combinatorial way and in course of doing so, we find a determinantal identity, which we think to be new.