notice the first diagonal all numbers are the digit 1
notice the second diagonal is increases by 1, this is because the following number in the pascal triangle is he number before in the second diagonal plus 1
the first number in the second diagonal is 1
then
the 14th number in the second diagonal is 14
the third diagonal is increasing by the sum of the second diagonal and the number before in the third diagonal
we can create the serie
![s=1+1+2+3+4+5+6+7+8+9+10+11+12+13+14](https://img.qammunity.org/2023/formulas/mathematics/college/armexsiy7nwrqn3j3089lpllzgpcuw4enh.png)
![s=105](https://img.qammunity.org/2023/formulas/mathematics/college/5csx4ehu9wajc4hjuehri8r6xsrkjrz4lz.png)
then the 14th number in the 3rd diagonal is 105