## A New Formula for the Sum of the Sixth Powers of Fibonacci Numbers

**Authors:** Hideyuki Ohtsuka, Shigeru Nakamura

Sloane's On-Line Encyclopedia of Integer Sequences incorrectly states
a lengthy formula for the sum of the sixth powers of the first n Fibonacci numbers.
In this paper we prove a more succinct formulation. We also provide an
analogue for the Lucas numbers. Finally, we prove a divisibility result for the
sum of certain even powers of the first n Fibonacci numbers.

**Comments:** 3 Pages, Published: Congressus Numerantum, Proceedings of the Thirteenth Conference
on Fibonacci Numbers and their Applications, Vol. 201, pp.297-300 (2010).

**Download:** **PDF**

### Submission history

[v1] 9 Oct 2009

**Unique-IP document downloads:** 561 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*