Pascal's triangle two ways

You will build a row of Pascal's triangle by adding neighbours, build it again from the formula, and check that each row adds up to a power of $2$. The checker tests rows $0$ to $12$.

The idea. Each new row starts with $1$, then holds the sums of neighbouring numbers of the row above, and ends with $1$. The formula gives the same row: ${}^nC_0, {}^nC_1, \dots, {}^nC_n$.

Your tasks.

1. Finish row_by_adding(n). Start from the row [1] and build one row at a time.
2. Finish row_by_formula(n). Use comb(n, k) for each k.
3. Finish row_sum(n). Add the numbers in row n.