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We all know fibonacci series, when k = 2. I.e.: 1,1,2,3,5,8,13 But this is the 2-fibonacci. Like this, I can count the third-fibonacci: 1,1,2,4,7,13,24 And the 4-fibonacci: 1,1,2,4,8,15,29 ...and so goes on What I'm asking is an algorithm to calculate an 'n' element inside a k-fibonacci series. Like this: if I ask for fibonacci(n=5,k=4) , the result should be: 8 , i.e. the fifth element inside the 4-fibonacci series. I didn't found it anywhere web. A resouce to help could be mathworld Anyone? And if you know python, I prefer. But if not, any language or algorithm can help. Tip I think that can help: Let's analyze the k-fibonacci series, where k will go from 1 to 5 k fibonacci series 1 1, 1, 1, 1, 1, 1, 1, 1,1, 1, 1, ... 2 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... 3 1, 1, 2, 4, 7, 13, 24, 44, 81, ... 4 1, 1, 2, 4, 8, 15, 29, 56, 108, ... 5 1, 1, 2, 4, 8, 16, 31, 61, 120, ... Analyzing this, we can see that the array [0:k] on the k-fibonacci series is equal to the previous fibonacci series, and it goes on till the k=1 i.e. (I'll try to show, but I'm not finding the right way to say it): k fibonacci series 1 1, 2 1, 1, 3 1, 1, 2, 4 1, 1, 2, 4, 5 1, 1, 2, 4, 8, Hope I've helped somehow to solve this. [SOLUTION in python (if anyone needs)] class Fibonacci: def __init__(self, k): self.cache = [] self.k = k #Bootstrap the cache self.cache.append(1) for i in range(1,k+1): self.cache.append(1 << (i-1)) def fib(self, n): #Extend cache until it includes value for n. #(If we've already compu

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