Formulas for linear sums that involve generalized Fibonacci and Lucas numbers

Zvonko Čerin

doi:10.5644/SJM.11.1.01

Authors

Zvonko Čerin

DOI:

https://doi.org/10.5644/SJM.11.1.01

Keywords:

(Generalized) Fibonacci number, (generalized) Lucas number, factor, sum, alternating, binomial coefient, product

Abstract

We extend Melham's formulas in [16] for certain classes of finite sums that involve generalized Fibonacci and Lucas numbers. We study the linear sums where only single terms of these numbers appear. Our results show that most of his formulas are the initial terms of a series of formulas, that the analogous and somewhat simpler identities hold for associated dual numbers and that besides the alternation according to the numbers ${(-1)^{\frac{n(n+1)}{2}}}$ it is possible to get similar formulas for the alternation according to the numbers ${(-1)^{\frac{n(n-1)}{2}}}$. We also consider sixteen linear sums with binomial coefficients that are products.

Statistics

Abstract: 17 / PDF: 8

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