Tessellate S.T.E.M.S - Computer Science - School - Set 2 - Problem 4

An integer valued function $f$ is defined by the following equations. If more than one equation apply, we choose the first one of them.

1. If $i = 0$ , $f(i,j) = 1$
2. If $i = 1$ , $f(i,j) = 1$
3. If $i > j$ , $f(i, j) = f(i-1, j)$
4. Otherwise, $f(i,j) = f(i - 1, j) + f(i - 2, j)$

Also, another integer valued function $g$ is defined as follows:

1. If $i = 0$ , $g(i,j) = f(0,j)$
2. Otherwise, $g(i, j) = g(i - 1, j) + f(i, j)$

Compute $g(9,10)$

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This problem is a part of Tessellate S.T.E.M.S.