# Problem 115: Counting block combinations II

![graphic](img115.gif)

NOTE: This is a more difficult version of Problem 114. A row measuring n
units in length has red blocks with a minimum length of m units placed
on it, such that any two red blocks (which are allowed to be different
lengths) are separated by at least one black square. Let the fill-count
function, F(m, n), represent the number of ways that a row can be
filled. For example, F(3, 29) = 673135 and F(3, 30) = 1089155. That is,
for m = 3, it can be seen that n = 30 is the smallest value for which
the fill-count function first exceeds one million. In the same way, for
m = 10, it can be verified that F(10, 56) = 880711 and F(10, 57) =
1148904, so n = 57 is the least value for which the fill-count function
first exceeds one million. For m = 50, find the least value of n for
which the fill-count function first exceeds one million.