Title

Counting Functions and Finite Differences

Document Type

Article

Publication Date

2007

Publication Title

Integers

Department

Mathematics and Computer Science

Abstract

Any increasing function p(d) on the natural numbers has an associated counting function ?(n) that yields the number of inputs d for which p(d)?n. In this article we derive three formulas that relate a sequence to its finite difference sequence by way of counting functions and the technique of summation by parts. We demonstrate our formulas by using them to produce several identities for Fibonacci numbers and binomial coefficients.

Volume

7

pp.

5914

ISSN

1867-0652