Some additive relations in the Pascal triangle

TL;DR

This paper explores new additive relations within Pascal's triangle, focusing on summing numbers along vertical lines and revealing interesting mathematical properties.

Contribution

It introduces novel additive relations in Pascal's triangle based on summing along vertical lines, which have not been previously documented.

Findings

Derived new additive relations in Pascal's triangle

Identified properties of sums along vertical lines

Revealed interesting mathematical patterns

Abstract

We derive some, seemingly new, curious additive relations in the Pascal triangle. They arise in summing up the numbers in the triangle along some vertical line up to some place.