Problem Statement
Consider the triangular array of numbers with 0,1,2,3,... along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row. Rows 1 through 6 are shown.\begin{tabular}{ccccccccccc} & & & & & 0 & & & & & \\ & & & & 1 & & 1 & & & & \\ & & & 2 & & 2 & & 2 & & & \\ & & 3 & & 4 & & 4 & & 3 & & \\ & 4 & & 7 & & 8 & & 7 & & 4 & \\ 5 & & 11 & & 15 & & 15 & & 11 & & 5 \end{tabular}Let f(n) denote the sum of the numbers in row n. What is the remainder when f(100) is divided by 100?<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 30<spanclass=′latex−bold′>(C)</span> 50<spanclass=′latex−bold′>(D)</span> 62<spanclass=′latex−bold′>(E)</span> 74