n steps with 1, 2 or 3 steps taken. How many ways to get to the top?

Question

If we have n steps and we can go up 1 or 2 steps at a time, there is a Fibonacci relation between the number of steps and the ways to climb them. IF and ONLY if we do not co

Answer 1

I would say that the formula will look in the following way:

K(1) = 1
K(2) = 2
k(3) = 4
K(n) = K(n-3) + K(n-2) + K(n - 1)

The formula says that in order to reach the n'th step we have to firstly reach:

• n-3'th step and then take 3 steps at once i.e. K(n-3)
• or n-2'th step and then take 2 steps at once i.e. K(n-2)
• or n-1'th step and then take 1 steps at once i.e. K(n-1)

K(4) = 7, K(5) = 13 etc.

You can either utilize the recursive formula or use dynamic programming.