Links Between Sums Over Paths in Bernoulli's Triangles and the Fibonacci Numbers

TL;DR

This paper explores the relationship between sums over paths in Bernoulli's triangles and Fibonacci numbers, revealing new connections and formulas linking these mathematical structures.

Contribution

It introduces novel relations connecting partial sums of binomial coefficients in Bernoulli's triangles to Fibonacci numbers.

Findings

Derived formulas linking path sums to Fibonacci numbers

Established new identities in Bernoulli's triangles

Enhanced understanding of combinatorial structures

Abstract

We investigate paths in Bernoulli's triangles, and derive several relations linking the partial sums of binomial coefficients to the Fibonacci numbers.