Exploring Pascal's Triangle
We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by $7$:
| $1$ | ||||||||||||
| $1$ | $1$ | |||||||||||
| $1$ | $2$ | $1$ | ||||||||||
| $1$ | $3$ | $3$ | $1$ | |||||||||
| $1$ | $4$ | $6$ | $4$ | $1$ | ||||||||
| $1$ | $5$ | $10$ | $10$ | $5$ | $1$ | |||||||
| $1$ | $6$ | $15$ | $20$ | $15$ | $6$ | $1$ |
However, if we check the first one hundred rows, we will find that only $2361$ of the $5050$ entries are not divisible by $7$.
Find the number of entries which are not divisible by $7$ in the first one billion ($10^9$) rows of Pascal's triangle.