Question

For solving the following recurrence relation, how many initial conditions are required? c(n) = c(n-1) + n*c(n-2) + (n-2)*c(n-3) + (n-3)*c(n-4) + 2

Answer 1

Answer: 4

Explanation:

To solve a recurrence relation of order k, we need k initial conditions.

In this case, the recurrence relation is:

c(n) = c(n-1) + n*c(n-2) + (n-2)*c(n-3) + (n-3)*c(n-4) + 2

We can see that this is a fourth-order recurrence relation, which means we need four initial conditions.

The initial conditions are values of c(0), c(1), c(2), and c(3), which are needed to determine the sequence c(n) for all values of n.

Therefore, we need four initial conditions to solve the recurrence relation c(n) = c(n-1) + n*c(n-2) + (n-2)*c(n-3) + (n-3)*c(n-4) + 2.