Question 147
In the pattern shown below, row 1 (the bottom row) consists of two $1$'s, and row $n$ is formed by taking row $n-1$ and inserting between each adjacent pair of numbers $a$ and $b$ their sum $a+b$:
| 1 | 5 | 4 | 7 | 3 | 8 | 5 | 7 | 2 | 7 | 5 | 8 | 3 | 7 | 4 | 5 | 1 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| 1 | | 4 | | 3 | | 5 | | 2 | | 5 | | 3 | | 4 | | 1 |
| 1 | | | | 3 | | | | 2 | | | | 3 | | | | 1 |
| 1 | | | | | | | | 2 | | | | | | | | 1 |
| 1 | | | | | | | | | | | | | | | 1 | |
| 1 | | | | | | | | | | | | | | | | |
In row 2019 of the pattern, how many copies of 2019 will there be?
| 1 | 5 | 4 | 7 | 3 | 8 | 5 | 7 | 2 | 7 | 5 | 8 | 3 | 7 | 4 | 5 | 1 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| 1 | | 4 | | 3 | | 5 | | 2 | | 5 | | 3 | | 4 | | 1 |
| 1 | | | | 3 | | | | 2 | | | | 3 | | | | 1 |
| 1 | | | | | | | | 2 | | | | | | | | 1 |
| 1 | | | | | | | | | | | | | | | 1 | |
| 1 | | | | | | | | | | | | | | | | |
In row 2019 of the pattern, how many copies of 2019 will there be?