Solving a Fibonacci like recurrence in log n time

Question

Finding the nth term in Fibonacci series f(n) = f(n-1) + f(n-2) can be solved in O(n) time by memoization.

A more efficient way would be to find the nth power of mat

Answer 1

You may want to look into Tribonacci numbers (and other generalizations of Fiboniacci numbers.) They have been studied quite extensively. See e.g. Generalizations of Fibonacci numbers