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A Novel Fibonacci Pattern in Pascal's Triangle

History and Overview 2018-11-07 v1

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 {1,12,0,12,1}\{-1,-\frac{1}{2},0, \frac{1}{2}, 1\}. A graphical illustration of this identity shows a novel "`beautiful"' Fibonacci pattern.

Keywords

Cite

@article{arxiv.1811.02085,
  title  = {A Novel Fibonacci Pattern in Pascal's Triangle},
  author = {Bernhard Moser},
  journal= {arXiv preprint arXiv:1811.02085},
  year   = {2018}
}

Comments

4 pages, 2 figures

R2 v1 2026-06-23T05:05:23.513Z