Binomial Sum Relations Involving Fibonacci and Lucas Numbers

Abstract

In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different kinds of binomial coefficients. We also present some novel relations between sums with two and three binomial coefficients. In the course of exploration, we rediscover a few isolated results existing in the literature, commonly presented as problem proposals.

Keywords

• binomial coefficient
• central binomial coefficient
• Fibonacci number
• Lucas number
• Horadam sequence
• recurrence relation