A Novel Fibonacci Pattern in Pascal's Triangle

TL;DR

This paper introduces a new Fibonacci pattern in Pascal's triangle achieved through a periodic weighted sum, revealing a visually appealing Fibonacci pattern.

Contribution

It presents a novel weighted sum method using a specific periodic pattern to generate Fibonacci numbers within Pascal's triangle.

Findings

A new Fibonacci pattern is identified in Pascal's triangle.

The pattern is achieved through a specific periodic weighting scheme.

Graphical illustration demonstrates the aesthetic Fibonacci pattern.

Abstract

The Fibonacci sequence is obtained as weighted sum along the rows in the Pascal triangle by choosing a periodic up-and-down pattern of weights from the set $\{-1,-\frac{1}{2},0, \frac{1}{2}, 1\}$. A graphical illustration of this identity shows a novel "`beautiful"' Fibonacci pattern.