Question 27
Consider the triangular array of numbers with $0,$ $1,$ $2,$ $3,$ $\ldots$ along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row. Rows $1$ through $6$ are shown.
$$
\begin{array}{cccccc} &&0&&&\\ &&1&1&&\\ &2&2&2&&\\ &3&4&4&3&\\ 4&7&8&7&4&\\ 5&11&15&15&11&5 \end{array}
$$
Let $f(n)$ denote the sum of the numbers in row $n.$ What is the remainder when $f(100)$ is divided by $100?$
$$
\begin{array}{cccccc} &&0&&&\\ &&1&1&&\\ &2&2&2&&\\ &3&4&4&3&\\ 4&7&8&7&4&\\ 5&11&15&15&11&5 \end{array}
$$
Let $f(n)$ denote the sum of the numbers in row $n.$ What is the remainder when $f(100)$ is divided by $100?$