Problem

Source: 2020 Dürer Math Competition Finals Day2 E6 https://artofproblemsolving.com/community/c1622639_2020_

Tags: algebra, Sum



We build a modified version of Pascal’s triangle as follows: in the first row we write a $2$ and a $3$, and in the further rows, every number is the sum of the two numbers directly above it (and rows always begin with a $2$ and end with a $3$). In the $13$th row, what is the $5$th number from the left?