See above, that's fairly close to what my code does.

Pardon me for rewriting in Python. My code runs without recursion and at about the same speed. def StairCaseMemo(N): memo = {} def stepsM(N): if N == 0: return 1 elif N<0: return 0 if N in memo.keys(): return memo[N] else: memo[N] = stepsM(N - 1) + stepsM(N - 2) + stepsM(N - 3); return memo[N]; print(stepsM(N)) def StairCaseMine(limit): # initial setup array = {} array[0] = 1 array[1] = array[2] = index = 0 while index < limit: count = array[index] array[index+1] += count array[index+2] += count array[index+3] = count index += 1 print(array[limit]) Enjoy!