2025 AMC 10A Problem 19

An array of numbers is constructed beginning with the numbers -1, 3, 1 in the top row. Each adjacent pair of numbers is summed to produce a number in the next row. Each row will begin and end with the numbers -1 and 1, respectively. The first three rows are shown below.

If the process continues, one of the rows will sum to 12{,}288. In that row, what is the third number from the left?

\textbf{(A)} -29 \qquad \textbf{(B)} -21 \qquad \textbf{(C)} -14 \qquad \textbf{(D)} -8 \qquad \textbf{(E)} -3

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.