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The challenge involves Fibonacci numbers or one of their generalizations.

Leonardo Fibonacci was a middle age mathematician (1180-1241 (about)), who is mostly known for the fibonacci-sequence 0, 1, 1, 2, 3, 5, 8, 13, ... which were formerly known in india and in the western antique.

The sequence starts with 0 and 1 and is generated by adding the last two numbers:

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
5 + 3 = 8 ...


It can also be described with the closed formula:

Which can be more concisely described by:

where

and