Partition Ways

Let's define a function $P(A)$ for a sequence $A$ as the number of ways to divide $A$ into contiguous subsequences such that each element of $A$ belongs to exactly one of these subsequences and the sum of elements of each subsequence is between $L$ and $R$ inclusive. For each integer $n$ between $1$ and $N$ inclusive, solve the following problem: Consider a random sequence $A$ with length $n$ w